114:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9.º EGB:@0.120102:0.967458:0.170641:0.967458:0.170641:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DUA:@0.070720:0.123711:0.114363:0.123711:0.114363:0.103460:0.070720:0.103460:0.000000:0.000000:0.000000
. Representación:@0.114363:0.123082:0.246653:0.123082:0.246653:0.106182:0.114363:0.106182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Trinomios cuadrados perfectos:@0.286308:0.079033:0.824180:0.079033:0.824180:0.042159:0.286308:0.042159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108604:0.183816:0.108604:0.183816:0.011516:0.094760:0.011516:0.000000:0.000000
En general, un trinomio es un polinomio que contiene tres términos.:@0.286308:0.157565:0.787681:0.157565:0.787681:0.141176:0.286308:0.141176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los trinomios son una parte fundamental de las matemáticas y tienen diversas apli-:@0.286308:0.181284:0.903114:0.181284:0.903114:0.164895:0.286308:0.164895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
caciones y utilidades en diferentes contextos, como la geometría, la ingeniería y :@0.286308:0.197880:0.907185:0.197880:0.907185:0.181491:0.286308:0.181491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
otras ciencias aplicadas. :@0.286308:0.214477:0.463930:0.214477:0.463930:0.198088:0.286308:0.198088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una expresión algebraica es un cuadrado perfecto cuando es el producto de dos :@0.286308:0.238196:0.907041:0.238196:0.907041:0.221807:0.286308:0.221807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
factores iguales. Por ejemplo, 64  es cuadrado perfecto de 8 ; y 25  es cuadrado :@0.286308:0.254792:0.907118:0.254802:0.907118:0.238413:0.286308:0.238403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.525884:0.254792:0.535153:0.254792:0.535153:0.238431:0.525884:0.238431:0.000000
2:@0.536073:0.248755:0.541315:0.248755:0.541315:0.239200:0.536073:0.239200:0.000000
a:@0.743934:0.254802:0.753203:0.254802:0.753203:0.238441:0.743934:0.238441:0.000000
x:@0.793080:0.254802:0.800543:0.254802:0.800543:0.238441:0.793080:0.238441:0.000000
2:@0.801444:0.248755:0.806687:0.248755:0.806687:0.239200:0.801444:0.239200:0.000000
perfecto de 5 .:@0.286309:0.271398:0.396359:0.271398:0.396359:0.255010:0.286309:0.255010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.384766:0.271398:0.392230:0.271398:0.392230:0.255037:0.384766:0.255037:0.000000
En este tema analizaremos la factorización de trinomios cuadrados perfectos.:@0.286309:0.295117:0.850319:0.295117:0.850319:0.278729:0.286309:0.278729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el diseño de la lámina de impresión radiográfica de la imagen, se ha usado la ex-:@0.286309:0.318836:0.903082:0.318836:0.903082:0.302448:0.286309:0.302448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presión  9:@0.286309:0.335433:0.361134:0.335444:0.361134:0.319055:0.286309:0.319044:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.381406:0.336122:0.349010:0.336122:0.349010:0.320549:0.381406:0.320549:0.000000
+:@0.423919:0.336122:0.391523:0.336122:0.391523:0.320549:0.423919:0.320549:0.000000
x:@0.362769:0.335444:0.370232:0.335444:0.370232:0.319083:0.362769:0.319083:0.000000
xyy:@0.405282:0.335444:0.445744:0.335444:0.445744:0.319083:0.405282:0.319083:0.000000:0.000000:0.000000
6:@0.394654:0.335444:0.403646:0.335444:0.403646:0.319055:0.394654:0.319055:0.000000
2:@0.371877:0.327783:0.377089:0.327783:0.377089:0.318285:0.371877:0.318285:0.000000
2:@0.447372:0.327783:0.452583:0.327783:0.452583:0.318285:0.447372:0.318285:0.000000
para  expresar su  área,  ¿es correcto decir  que la  placa es :@0.456740:0.335444:0.907156:0.335444:0.907156:0.319055:0.456740:0.319055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuadrada?:@0.286303:0.352041:0.361911:0.352041:0.361911:0.335652:0.286303:0.335652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dado que el área del cuadrado se obtiene elevando su lado al cuadrado, debemos de-:@0.286303:0.375759:0.903131:0.375759:0.903131:0.359371:0.286303:0.359371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
terminar la expresión que representa el área que resulta de esta operación. Para ello, :@0.286303:0.392356:0.907185:0.392356:0.907185:0.375967:0.286303:0.375967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
vamos a conceptualizar lo que es un trinomio cuadrado perfecto.:@0.286303:0.408952:0.752852:0.408952:0.752852:0.392563:0.286303:0.392563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un trinomio cuadrado perfecto (TCP) es un polinomio ordenado en relación con :@0.295805:0.439917:0.897541:0.439917:0.897541:0.423528:0.295805:0.423528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una variable; es cuadrado perfecto cuando el primer y tercer términos son cuadra-:@0.295805:0.456513:0.893501:0.456513:0.893501:0.440124:0.295805:0.440124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos perfectos (o tienen la raíz cuadrada exacta) y positivos. Además, el segundo :@0.295805:0.473110:0.897574:0.473110:0.897574:0.456721:0.295805:0.456721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
término equivale al doble del producto de estas raíces cuadradas.:@0.295805:0.489706:0.775599:0.489706:0.775599:0.473317:0.295805:0.473317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.565481:0.513185:0.575598:0.513185:0.575598:0.497612:0.565481:0.497612:0.000000
+:@0.608823:0.513185:0.618940:0.513185:0.618940:0.497612:0.608823:0.497612:0.000000
a:@0.546114:0.512507:0.555383:0.512507:0.555383:0.496146:0.546114:0.496146:0.000000
abb:@0.587521:0.512507:0.630973:0.512507:0.630973:0.496146:0.587521:0.496146:0.000000:0.000000:0.000000
2:@0.578361:0.512507:0.587353:0.512507:0.587353:0.496838:0.578361:0.496838:0.000000
2:@0.555941:0.504855:0.561153:0.504855:0.561153:0.495774:0.555941:0.495774:0.000000
2:@0.631532:0.504855:0.636743:0.504855:0.636743:0.495774:0.631532:0.495774:0.000000
Esta  expresión  se  obtiene  al desarrollar el  cuadrado  de un binomio. :@0.295805:0.533798:0.897649:0.533798:0.897649:0.517410:0.295805:0.517410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por lo tanto:  :@0.295805:0.550395:0.392200:0.550395:0.392200:0.534006:0.295805:0.534006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.618566:0.571064:0.624703:0.571064:0.624703:0.550664:0.618566:0.550664:0.000000
):@0.661024:0.571064:0.667160:0.571064:0.667160:0.550664:0.661024:0.550664:0.000000
+:@0.529464:0.569193:0.539580:0.569193:0.539580:0.553620:0.529464:0.553620:0.000000
+:@0.572805:0.569193:0.582922:0.569193:0.582922:0.553620:0.572805:0.553620:0.000000
=:@0.605588:0.569193:0.615705:0.569193:0.615705:0.553620:0.605588:0.553620:0.000000
+:@0.637892:0.569193:0.648009:0.569193:0.648009:0.553620:0.637892:0.553620:0.000000
a:@0.510095:0.568515:0.519364:0.568515:0.519364:0.552154:0.510095:0.552154:0.000000
abb:@0.551501:0.568515:0.594957:0.568515:0.594957:0.552154:0.551501:0.552154:0.000000:0.000000:0.000000
ab:@0.625787:0.568515:0.660025:0.568515:0.660025:0.552154:0.625787:0.552154:0.000000:0.000000
2:@0.542346:0.568515:0.551339:0.568515:0.551339:0.552845:0.542346:0.552845:0.000000
2:@0.519937:0.560863:0.525148:0.560863:0.525148:0.551782:0.519937:0.551782:0.000000
2:@0.595527:0.560863:0.600739:0.560863:0.600739:0.551782:0.595527:0.551782:0.000000
2:@0.667043:0.559095:0.672254:0.559095:0.672254:0.550014:0.667043:0.550014:0.000000
De acuerdo con esta información, determinamos si la expresión 9:@0.286308:0.614964:0.764671:0.614943:0.764671:0.598554:0.286308:0.598575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.784943:0.615621:0.752547:0.615621:0.752547:0.600048:0.784943:0.600048:0.000000
+:@0.827455:0.615621:0.795060:0.615621:0.795060:0.600048:0.827455:0.600048:0.000000
x:@0.766306:0.614943:0.773769:0.614943:0.773769:0.598582:0.766306:0.598582:0.000000
xyy:@0.808818:0.614943:0.849280:0.614943:0.849280:0.598582:0.808818:0.598582:0.000000:0.000000:0.000000
6:@0.798191:0.614943:0.807183:0.614943:0.807183:0.598554:0.798191:0.598554:0.000000
2:@0.775416:0.607282:0.780627:0.607282:0.780627:0.597784:0.775416:0.597784:0.000000
2:@0.850910:0.607282:0.856122:0.607282:0.856122:0.597784:0.850910:0.597784:0.000000
 es un :@0.860277:0.614964:0.907120:0.614964:0.907120:0.598575:0.860277:0.598575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trinomio cuadrado perfecto::@0.286311:0.631560:0.493581:0.631560:0.493581:0.615171:0.286311:0.615171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.563964:0.657219:0.510100:0.657219:0.510100:0.641646:0.563964:0.641646:0.000000
+:@0.627944:0.657219:0.574080:0.657219:0.574080:0.641646:0.627944:0.641646:0.000000
x:@0.535903:0.656541:0.543367:0.656541:0.543367:0.640180:0.535903:0.640180:0.000000
xy:@0.599884:0.656541:0.614635:0.656541:0.614635:0.640180:0.599884:0.640180:0.000000:0.000000
y:@0.649094:0.656541:0.656576:0.656541:0.656576:0.640180:0.649094:0.640180:0.000000
9:@0.525276:0.656541:0.534268:0.656541:0.534268:0.640152:0.525276:0.640152:0.000000
6:@0.589256:0.656541:0.598249:0.656541:0.598249:0.640152:0.589256:0.640152:0.000000
2:@0.545013:0.648880:0.550225:0.648880:0.550225:0.639382:0.545013:0.639382:0.000000
2:@0.658196:0.648880:0.663408:0.648880:0.663408:0.639382:0.658196:0.639382:0.000000
x x:@0.535871:0.687809:0.566448:0.687954:0.566448:0.671592:0.535871:0.671448:0.000000:0.000000:0.000000
y y:@0.625817:0.687809:0.656412:0.687954:0.656412:0.671592:0.625817:0.671448:0.000000:0.000000:0.000000
3 3:@0.526029:0.687809:0.558137:0.687954:0.558137:0.671565:0.526029:0.671420:0.000000:0.000000:0.000000
2:@0.634920:0.680148:0.640132:0.680148:0.640132:0.670650:0.634920:0.670650:0.000000
                    :@0.554339:0.694240:0.635052:0.694240:0.635052:0.677851:0.554339:0.677851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.658033:0.680291:0.663245:0.680291:0.663245:0.670793:0.658033:0.670793:0.000000
xy:@0.595374:0.716707:0.618409:0.716707:0.618409:0.700346:0.595374:0.700346:0.000000:0.000000
2(3):@0.571455:0.716707:0.609785:0.716707:0.609785:0.700318:0.571455:0.700318:0.000000:0.000000:0.000000:0.000000
xy:@0.591553:0.745460:0.606314:0.745460:0.606314:0.729099:0.591553:0.729099:0.000000:0.000000
6:@0.580920:0.745460:0.589913:0.745460:0.589913:0.729071:0.580920:0.729071:0.000000
Regla para factorizar un trinomio cuadrado perfecto:@0.286308:0.771448:0.706546:0.771448:0.706546:0.754548:0.286308:0.754548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: se extrae la raíz cuadrada :@0.706546:0.771448:0.907131:0.771448:0.907131:0.755060:0.706546:0.755060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del primer y tercer términos del trinomio y se separan estas raíces por el signo del se-:@0.286308:0.788045:0.903171:0.788045:0.903171:0.771656:0.286308:0.771656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gundo término. El binomio  ya formado, que es la raíz cuadrada del trinomio,:@0.286308:0.804641:0.903162:0.804641:0.903162:0.788252:0.286308:0.788252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se multiplica por sí mismo o se eleva al cuadrado.:@0.286308:0.821238:0.647464:0.821238:0.647464:0.804849:0.286308:0.804849:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.318187:0.846893:0.328304:0.846893:0.328304:0.831320:0.318187:0.831320:0.000000
+:@0.360700:0.846893:0.370817:0.846893:0.370817:0.831320:0.360700:0.831320:0.000000
=:@0.394203:0.846897:0.404320:0.846897:0.404320:0.831324:0.394203:0.831324:0.000000
+:@0.434099:0.846897:0.444216:0.846897:0.444216:0.831324:0.434099:0.831324:0.000000
x:@0.299552:0.846219:0.307015:0.846219:0.307015:0.829858:0.299552:0.829858:0.000000
xyy:@0.342065:0.846219:0.382532:0.846219:0.382532:0.829858:0.342065:0.829858:0.000000:0.000000:0.000000
xy:@0.422734:0.846219:0.455922:0.846219:0.455922:0.829858:0.422734:0.829858:0.000000:0.000000
9:@0.288924:0.846219:0.297917:0.846219:0.297917:0.829830:0.288924:0.829830:0.000000
6:@0.331437:0.846219:0.340430:0.846219:0.340430:0.829830:0.331437:0.829830:0.000000
(3:@0.407193:0.846219:0.421898:0.846219:0.421898:0.829830:0.407193:0.829830:0.000000:0.000000
):@0.457980:0.846219:0.462863:0.846219:0.462863:0.829830:0.457980:0.829830:0.000000
2:@0.308660:0.838558:0.313872:0.838558:0.313872:0.829060:0.308660:0.829060:0.000000
2:@0.384155:0.838558:0.389367:0.838558:0.389367:0.829060:0.384155:0.829060:0.000000
2:@0.462832:0.838558:0.468044:0.838558:0.468044:0.829060:0.462832:0.829060:0.000000
El resultado obtenido nos permite deducir que la forma de la lámina de impresión :@0.286308:0.876229:0.907133:0.876229:0.907133:0.859840:0.286308:0.859840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
radiográfica es la de un cuadrado, cuyo lado queda representado por la expresión :@0.286308:0.892826:0.907061:0.892826:0.907061:0.876437:0.286308:0.876437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algebraica  3:@0.286308:0.909464:0.377598:0.908165:0.377598:0.891776:0.286308:0.893075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.389816:0.908841:0.399932:0.908841:0.399932:0.893268:0.389816:0.893268:0.000000
xy:@0.378446:0.908165:0.411634:0.908165:0.411634:0.891804:0.378446:0.891804:0.000000:0.000000
.:@0.412787:0.908205:0.415993:0.908205:0.415993:0.891816:0.412787:0.891816:0.000000
Las expresiones :@0.140274:0.544649:0.248425:0.544649:0.248425:0.529750:0.140274:0.529750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algebraicas son una :@0.112783:0.559737:0.248427:0.559737:0.248427:0.544838:0.112783:0.544838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
especie de lenguaje :@0.111359:0.574824:0.248427:0.574824:0.248427:0.559925:0.111359:0.559925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemático, que se :@0.113420:0.589912:0.248425:0.589912:0.248425:0.575013:0.113420:0.575013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emplean para representar :@0.072577:0.604999:0.248425:0.604999:0.248425:0.590100:0.072577:0.590100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
situaciones y relaciones. :@0.085376:0.620087:0.248425:0.620087:0.248425:0.605188:0.085376:0.605188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Son básicas para entender :@0.069210:0.635175:0.248425:0.635175:0.248425:0.620276:0.069210:0.620276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
problemas de manera :@0.097790:0.650262:0.248427:0.650262:0.248427:0.635363:0.097790:0.635363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
abstracta, lo que es :@0.116636:0.665350:0.248425:0.665350:0.248425:0.650451:0.116636:0.650451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
permite resolver :@0.136119:0.680437:0.248425:0.680437:0.248425:0.665538:0.136119:0.665538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
situaciones en ámbitos :@0.091340:0.695525:0.248425:0.695525:0.248425:0.680626:0.091340:0.680626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como física o economía.:@0.082964:0.710613:0.244758:0.710613:0.244758:0.695714:0.082964:0.695714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
    Comunicacional:@0.101541:0.512208:0.237601:0.512208:0.237601:0.495307:0.101541:0.495307:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.064206:0.801084:0.064206:0.795977:0.052125:0.795977:0.052125:0.801084:0.000000
Shutterstock:@0.064206:0.795977:0.064206:0.758259:0.052295:0.758259:0.052295:0.795977:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Álgebra y computación:@0.076615:0.195794:0.244757:0.195794:0.244757:0.180430:0.076615:0.180430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El álgebra computacional :@0.074872:0.214440:0.248427:0.214440:0.248427:0.199541:0.074872:0.199541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es esencial en el :@0.136990:0.229528:0.248427:0.229528:0.248427:0.214629:0.136990:0.214629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
desarrollo de algoritmos :@0.082545:0.244615:0.248426:0.244615:0.248426:0.229716:0.082545:0.229716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que manipulan :@0.142904:0.259703:0.248427:0.259703:0.248427:0.244804:0.142904:0.244804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
expresiones algebraicas, :@0.083885:0.274791:0.248424:0.274791:0.248424:0.259892:0.083885:0.259892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
crucial para áreas como :@0.087554:0.289878:0.248426:0.289878:0.248426:0.274979:0.087554:0.274979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inteligencia artificial y :@0.100839:0.304966:0.248426:0.304966:0.248426:0.290067:0.100839:0.290067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
análisis de datos:@0.135985:0.320054:0.244757:0.320054:0.244757:0.305154:0.135985:0.305154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.091880:0.166635:0.245583:0.166635:0.245583:0.149734:0.091880:0.149734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 M.4.1.33. :@0.290067:0.965521:0.340832:0.965521:0.340832:0.954766:0.290067:0.954766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconocer y calcular productos notables e identificar factores de expresiones algebraicas.:@0.340832:0.965521:0.757440:0.965521:0.757440:0.955091:0.340832:0.955091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.571269:0.965521:0.573837:0.965521:0.573837:0.955091:0.571269:0.955091:0.000000