110:@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
Factorización de binomios:@0.286308:0.079033:0.743246:0.079033:0.743246:0.042159:0.286308:0.042159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108604:0.183816:0.108604:0.183816:0.011516:0.094760:0.011516:0.000000:0.000000
No todos los polinomios contienen un factor común; así que, de no ser aplicable :@0.287495:0.153866:0.907143:0.153866:0.907143:0.137477:0.287495:0.137477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
esta técnica, se deben verificar otras propiedades de los polinomios para emplear :@0.287495:0.170462:0.907068:0.170462:0.907068:0.154073:0.287495:0.154073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
otro método de factorización. Por ejemplo, si analizamos el binomio x² – 1, no se :@0.287495:0.187059:0.907130:0.187059:0.907130:0.170670:0.287495:0.170670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puede factorizar mediante factor común, pero si recordamos los productos nota-:@0.287495:0.203655:0.903085:0.203655:0.903085:0.187266:0.287495:0.187266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bles, se tiene que (x +1)(x – 1) = x2 – 1.:@0.287495:0.220251:0.565697:0.220251:0.565697:0.203863:0.287495:0.203863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Veamos un ejemplo.:@0.287495:0.243970:0.436868:0.243970:0.436868:0.227582:0.287495:0.227582:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La red de comunicación celular comprende algunos elementos, entre ellos el de :@0.287495:0.267689:0.907198:0.267689:0.907198:0.251301:0.287495:0.251301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
acceso al público (el teléfono celular). En el diseño de un teléfono celular se ha :@0.287495:0.284286:0.907178:0.284286:0.907178:0.267897:0.287495:0.267897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
considerado la expresión :@0.287495:0.301892:0.478756:0.301892:0.478756:0.285503:0.287495:0.285503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.503504:0.301311:0.513621:0.301311:0.513621:0.285738:0.503504:0.285738:0.000000
x:@0.484876:0.300642:0.492339:0.300642:0.492339:0.284281:0.484876:0.284281:0.000000
y:@0.517861:0.300642:0.525343:0.300642:0.525343:0.284281:0.517861:0.284281:0.000000
2:@0.493984:0.292980:0.499195:0.292980:0.499195:0.283482:0.493984:0.283482:0.000000
2:@0.526963:0.292980:0.532174:0.292980:0.532174:0.283482:0.526963:0.283482:0.000000
 para representar el área de su parte rectangular :@0.536074:0.301899:0.907133:0.301899:0.907133:0.285510:0.536074:0.285510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
frontal. ¿Es posible encontrar una expresión que represente su largo y otra que :@0.287485:0.318496:0.907059:0.318496:0.907059:0.302107:0.287485:0.302107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
represente su ancho?:@0.287485:0.335092:0.444100:0.335092:0.444100:0.318703:0.287485:0.318703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De acuerdo con los productos notables, cuando multiplicamos la suma de dos tér-:@0.287485:0.358811:0.903156:0.358811:0.903156:0.342422:0.287485:0.342422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
minos por su diferencia, obtenemos la diferencia de sus cuadrados. Como :@0.287485:0.375407:0.907113:0.375407:0.907113:0.359019:0.287485:0.359019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la factorización es un proceso contrario a la multiplicación, podemos decir que::@0.287485:0.392004:0.866773:0.392004:0.866773:0.375615:0.287485:0.375615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.310207:0.419817:0.320323:0.419817:0.320323:0.404244:0.310207:0.404244:0.000000
x:@0.291578:0.419139:0.299041:0.419139:0.299041:0.402778:0.291578:0.402778:0.000000
y:@0.324563:0.419139:0.332045:0.419139:0.332045:0.402778:0.324563:0.402778:0.000000
2:@0.300688:0.411478:0.305900:0.411478:0.305900:0.401980:0.300688:0.401980:0.000000
2:@0.333667:0.411478:0.338878:0.411478:0.338878:0.401980:0.333667:0.401980:0.000000
=:@0.346812:0.420396:0.357795:0.420396:0.357795:0.404007:0.346812:0.404007:0.000000
(:@0.364030:0.422054:0.370167:0.422054:0.370167:0.401653:0.364030:0.401653:0.000000
)(:@0.407593:0.422054:0.420161:0.422054:0.420161:0.401653:0.407593:0.401653:0.000000:0.000000
):@0.457588:0.422054:0.463724:0.422054:0.463724:0.401653:0.457588:0.401653:0.000000
+:@0.383714:0.420182:0.393831:0.420182:0.393831:0.404610:0.383714:0.404610:0.000000
−:@0.433709:0.420182:0.443825:0.420182:0.443825:0.404610:0.433709:0.404610:0.000000
xy xy:@0.372355:0.419505:0.455537:0.419505:0.455537:0.403144:0.372355:0.403144:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.463067:0.420396:0.466274:0.420396:0.466274:0.404007:0.463067:0.404007:0.000000
Por lo tanto, diremos que la expresión que representa al largo es   + :@0.287489:0.449149:0.787165:0.449149:0.787165:0.432760:0.287489:0.432760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.760648:0.449149:0.768111:0.449149:0.768111:0.432788:0.760648:0.432788:0.000000
y:@0.787165:0.449149:0.794647:0.449149:0.794647:0.432788:0.787165:0.432788:0.000000
 y la que representa al ancho es (  –  .:@0.287489:0.465746:0.566555:0.465746:0.566555:0.449357:0.287489:0.449357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y):@0.526235:0.465746:0.563349:0.465746:0.563349:0.449385:0.526235:0.449385:0.000000:0.000000:0.000000:0.000000
La diferencia de dos cuadrados perfectos es igual a dos factores: uno formado por :@0.296992:0.500269:0.897582:0.500269:0.897582:0.483880:0.296992:0.483880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la suma de sus raíces cuadradas, y el otro, por la diferencia de esas raíces.:@0.296992:0.516865:0.827113:0.516865:0.827113:0.500476:0.296992:0.500476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.543606:0.540174:0.553622:0.540174:0.553622:0.524757:0.543606:0.524757:0.000000
=:@0.576043:0.540174:0.586058:0.540174:0.586058:0.524757:0.576043:0.524757:0.000000
+:@0.606888:0.540174:0.616904:0.540174:0.616904:0.524757:0.606888:0.524757:0.000000
−:@0.652351:0.540174:0.662366:0.540174:0.662366:0.524757:0.652351:0.524757:0.000000
a:@0.524428:0.539503:0.533605:0.539503:0.533605:0.523306:0.524428:0.523306:0.000000
b:@0.556354:0.539503:0.565531:0.539503:0.565531:0.523306:0.556354:0.523306:0.000000
ab ab:@0.594921:0.539503:0.674261:0.539503:0.674261:0.523306:0.594921:0.523306:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.588905:0.539503:0.593739:0.539503:0.593739:0.523990:0.588905:0.523990:0.000000
)(:@0.629806:0.539503:0.639192:0.539503:0.639192:0.523990:0.629806:0.523990:0.000000:0.000000
):@0.675259:0.539503:0.680093:0.539503:0.680093:0.523990:0.675259:0.523990:0.000000
2:@0.534174:0.531927:0.539334:0.531927:0.539334:0.522937:0.534174:0.522937:0.000000
2:@0.566105:0.531927:0.571264:0.531927:0.571264:0.522937:0.566105:0.522937:0.000000
Ejemplos::@0.287495:0.584856:0.357852:0.584856:0.357852:0.568218:0.287495:0.568218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a)  :@0.287495:0.608990:0.310032:0.608990:0.310032:0.592089:0.287495:0.592089:0.000000:0.000000:0.000000:0.000000
Factoriza 16:@0.311230:0.608990:0.399515:0.608996:0.399515:0.592607:0.311230:0.592601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.419787:0.609668:0.429904:0.609668:0.429904:0.594095:0.419787:0.594095:0.000000
x:@0.401155:0.608996:0.408619:0.608996:0.408619:0.592635:0.401155:0.592635:0.000000
y:@0.452827:0.608996:0.460308:0.608996:0.460308:0.592635:0.452827:0.592635:0.000000
49:@0.433404:0.608996:0.451186:0.608996:0.451186:0.592607:0.433404:0.592607:0.000000:0.000000
2:@0.410264:0.601335:0.415475:0.601335:0.415475:0.591837:0.410264:0.591837:0.000000
2:@0.461932:0.601335:0.467144:0.601335:0.467144:0.591837:0.461932:0.591837:0.000000
Solución:@0.287495:0.639849:0.351273:0.639849:0.351273:0.623211:0.287495:0.623211:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Comprobamos que 16:@0.287495:0.671120:0.454483:0.671117:0.454483:0.654728:0.287495:0.654731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.456123:0.671117:0.463587:0.671117:0.463587:0.654756:0.456123:0.654756:0.000000
2:@0.465232:0.663456:0.470443:0.663456:0.470443:0.653958:0.465232:0.653958:0.000000
 y  49:@0.473765:0.671117:0.511229:0.669859:0.511229:0.653470:0.473765:0.654728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.512869:0.669859:0.520350:0.669859:0.520350:0.653497:0.512869:0.653497:0.000000
2:@0.521982:0.662199:0.527194:0.662199:0.527194:0.652701:0.521982:0.652701:0.000000
sean cuadrados perfectos, es decir, calculamos sus :@0.534419:0.671117:0.907098:0.671117:0.907098:0.654728:0.534419:0.654728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
raíces cuadradas exactas.:@0.287489:0.687713:0.470269:0.687713:0.470269:0.671325:0.287489:0.671325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De 16:@0.287489:0.718984:0.331749:0.719150:0.331749:0.702761:0.287489:0.702595:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.333389:0.719150:0.340852:0.719150:0.340852:0.702789:0.333389:0.702789:0.000000
2:@0.342497:0.711489:0.347709:0.711489:0.347709:0.701991:0.342497:0.701991:0.000000
es 4  y de 49:@0.355066:0.718983:0.462030:0.718983:0.462030:0.702594:0.355066:0.702594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.389256:0.718983:0.396719:0.718983:0.396719:0.702621:0.389256:0.702621:0.000000
y:@0.463670:0.718983:0.471152:0.718983:0.471152:0.702621:0.463670:0.702621:0.000000
2:@0.472774:0.711320:0.477985:0.711320:0.477985:0.701822:0.472774:0.701822:0.000000
 es 7 .:@0.481098:0.718983:0.530120:0.718983:0.530120:0.702594:0.481098:0.702594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.517806:0.718983:0.525287:0.718983:0.525287:0.702621:0.517806:0.702621:0.000000
Como tales raíces existen, factorizamos aplicando la regla::@0.287502:0.749838:0.709985:0.749838:0.709985:0.733449:0.287502:0.733449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@0.327029:0.775493:0.337146:0.775493:0.337146:0.759920:0.327029:0.759920:0.000000
=:@0.379216:0.775493:0.389333:0.775493:0.389333:0.759920:0.379216:0.759920:0.000000
+:@0.420990:0.775493:0.431107:0.775493:0.431107:0.759920:0.420990:0.759920:0.000000
−:@0.486998:0.775493:0.497115:0.775493:0.497115:0.759920:0.486998:0.759920:0.000000
x:@0.308382:0.774816:0.315846:0.774816:0.315846:0.758454:0.308382:0.758454:0.000000
y:@0.360053:0.774816:0.367535:0.774816:0.367535:0.758454:0.360053:0.758454:0.000000
x:@0.409624:0.774816:0.417087:0.774816:0.417087:0.758454:0.409624:0.758454:0.000000
y:@0.444065:0.774816:0.451547:0.774816:0.451547:0.758454:0.444065:0.758454:0.000000
x:@0.475645:0.774816:0.483108:0.774816:0.483108:0.758454:0.475645:0.758454:0.000000
y:@0.510086:0.774816:0.517568:0.774816:0.517568:0.758454:0.510086:0.758454:0.000000
16:@0.288961:0.774816:0.306744:0.774816:0.306744:0.758427:0.288961:0.758427:0.000000:0.000000
49:@0.340632:0.774816:0.358415:0.774816:0.358415:0.758427:0.340632:0.758427:0.000000:0.000000
(4:@0.392193:0.774816:0.407617:0.774816:0.407617:0.758427:0.392193:0.758427:0.000000:0.000000
7)(4:@0.433452:0.774816:0.473643:0.774816:0.473643:0.758427:0.433452:0.758427:0.000000:0.000000:0.000000:0.000000
7):@0.499465:0.774816:0.524508:0.774816:0.524508:0.758427:0.499465:0.758427:0.000000:0.000000
2:@0.317492:0.767155:0.322704:0.767155:0.322704:0.757656:0.317492:0.757656:0.000000
2:@0.369160:0.767155:0.374372:0.767155:0.374372:0.757656:0.369160:0.757656:0.000000
Red de comunicación.:@0.106302:0.390045:0.254997:0.390045:0.254997:0.375146:0.106302:0.375146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.075544:0.351782:0.075544:0.346674:0.063462:0.346674:0.063462:0.351782:0.000000
Shutterstock:@0.075544:0.346674:0.075544:0.308956:0.063633:0.308956:0.063633:0.346674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b)  :@0.287495:0.826346:0.311341:0.826346:0.311341:0.809445:0.287495:0.809445:0.000000:0.000000:0.000000:0.000000
Factoriza  4:@0.311230:0.826346:0.392349:0.826771:0.392349:0.810382:0.311230:0.809957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9:@0.430420:0.818010:0.439413:0.818010:0.439413:0.801621:0.430420:0.801621:0.000000
16:@0.425389:0.837621:0.443283:0.837621:0.443283:0.821233:0.425389:0.821233:0.000000:0.000000
2:@0.402779:0.819110:0.407990:0.819110:0.407990:0.809612:0.402779:0.809612:0.000000
2:@0.457117:0.819110:0.462328:0.819110:0.462328:0.809612:0.457117:0.809612:0.000000
x:@0.393721:0.826771:0.401184:0.826771:0.401184:0.810410:0.393721:0.810410:0.000000
y:@0.448064:0.826771:0.455545:0.826771:0.455545:0.810410:0.448064:0.810410:0.000000
−:@0.412673:0.826356:0.422789:0.826356:0.422789:0.809414:0.412673:0.809414:0.000000
Solución:@0.287494:0.864320:0.351272:0.864320:0.351272:0.847682:0.287494:0.847682:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.290583:0.898109:0.299576:0.898109:0.299576:0.881720:0.290583:0.881720:0.000000
9:@0.337647:0.889341:0.346640:0.889341:0.346640:0.872952:0.337647:0.872952:0.000000
16:@0.332616:0.908952:0.350510:0.908952:0.350510:0.892563:0.332616:0.892563:0.000000:0.000000
2:@0.396947:0.898109:0.405940:0.898109:0.405940:0.881720:0.396947:0.881720:0.000000
3:@0.433065:0.889341:0.442058:0.889341:0.442058:0.872952:0.433065:0.872952:0.000000
4:@0.433065:0.908952:0.442058:0.908952:0.442058:0.892563:0.433065:0.892563:0.000000
2:@0.475265:0.898109:0.484257:0.898109:0.484257:0.881720:0.475265:0.881720:0.000000
3:@0.511070:0.889341:0.520062:0.889341:0.520062:0.872952:0.511070:0.872952:0.000000
4:@0.511070:0.908952:0.520062:0.908952:0.520062:0.892563:0.511070:0.892563:0.000000
2:@0.310006:0.890448:0.315217:0.890448:0.315217:0.880950:0.310006:0.880950:0.000000
2:@0.364344:0.890448:0.369555:0.890448:0.369555:0.880950:0.364344:0.880950:0.000000
x:@0.300949:0.898109:0.308412:0.898109:0.308412:0.881748:0.300949:0.881748:0.000000
y:@0.355292:0.898109:0.362774:0.898109:0.362774:0.881748:0.355292:0.881748:0.000000
x:@0.406742:0.898109:0.414206:0.898109:0.414206:0.881748:0.406742:0.881748:0.000000
y:@0.446841:0.898109:0.454322:0.898109:0.454322:0.881748:0.446841:0.881748:0.000000
x:@0.485068:0.898109:0.492531:0.898109:0.492531:0.881748:0.485068:0.881748:0.000000
y:@0.524853:0.898109:0.532335:0.898109:0.532335:0.881748:0.524853:0.881748:0.000000
−:@0.319900:0.897694:0.330016:0.897694:0.330016:0.880752:0.319900:0.880752:0.000000
=:@0.374869:0.897694:0.384986:0.897694:0.384986:0.880752:0.374869:0.880752:0.000000
+:@0.418322:0.897694:0.428438:0.897694:0.428438:0.880752:0.418322:0.880752:0.000000
:@0.387898:0.890184:0.394974:0.890184:0.394974:0.873242:0.387898:0.873242:0.000000
:@0.387904:0.909953:0.394980:0.909953:0.394980:0.893011:0.387904:0.893011:0.000000
:@0.387904:0.901270:0.394980:0.901270:0.394980:0.884328:0.387904:0.884328:0.000000
:@0.457579:0.890192:0.473285:0.890178:0.473285:0.873236:0.457579:0.873250:0.000000:0.000000
:@0.457584:0.909953:0.473298:0.909953:0.473298:0.893011:0.457584:0.893011:0.000000:0.000000
:@0.457584:0.901270:0.473298:0.901270:0.473298:0.884328:0.457584:0.884328:0.000000:0.000000
−:@0.496632:0.897688:0.506749:0.897688:0.506749:0.880746:0.496632:0.880746:0.000000
:@0.535583:0.890192:0.542660:0.890192:0.542660:0.873250:0.535583:0.873250:0.000000
:@0.535587:0.909953:0.542663:0.909953:0.542663:0.893011:0.535587:0.893011:0.000000
:@0.535587:0.901270:0.542663:0.901270:0.542663:0.884328:0.535587:0.884328:0.000000
c)  :@0.621681:0.826628:0.643130:0.826628:0.643130:0.809727:0.621681:0.809727:0.000000:0.000000:0.000000:0.000000
Factoriza :@0.645415:0.826628:0.714443:0.826628:0.714443:0.810239:0.645415:0.810239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.718370:0.826780:0.725834:0.826780:0.725834:0.810418:0.718370:0.810418:0.000000
2:@0.727440:0.819110:0.732652:0.819110:0.732652:0.809612:0.727440:0.809612:0.000000
5:@0.749743:0.826771:0.758735:0.826771:0.758735:0.810382:0.749743:0.810382:0.000000
−:@0.737341:0.826356:0.747458:0.826356:0.747458:0.809414:0.737341:0.809414:0.000000
Solución:@0.621689:0.864182:0.685467:0.864182:0.685467:0.847544:0.621689:0.847544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.625611:0.891684:0.633074:0.891684:0.633074:0.875323:0.625611:0.875323:0.000000
x:@0.690052:0.891684:0.697515:0.891684:0.697515:0.875323:0.690052:0.875323:0.000000
x:@0.753554:0.891684:0.761017:0.891684:0.761017:0.875323:0.753554:0.875323:0.000000
2:@0.634669:0.884022:0.639880:0.884022:0.639880:0.874524:0.634669:0.874524:0.000000
5:@0.656970:0.891684:0.665962:0.891684:0.665962:0.875295:0.656970:0.875295:0.000000
5:@0.726866:0.891684:0.735858:0.891684:0.735858:0.875295:0.726866:0.875295:0.000000
5:@0.790054:0.891684:0.799047:0.891684:0.799047:0.875295:0.790054:0.875295:0.000000
−=:@0.644568:0.891269:0.678714:0.891269:0.678714:0.874327:0.644568:0.874327:0.000000:0.000000
+:@0.701638:0.891269:0.711755:0.891269:0.711755:0.874327:0.701638:0.874327:0.000000
(:@0.681627:0.895915:0.687764:0.895915:0.687764:0.866232:0.681627:0.866232:0.000000
)(:@0.737647:0.895915:0.751265:0.895915:0.751265:0.866232:0.737647:0.866232:0.000000:0.000000
−:@0.765128:0.891269:0.775245:0.891269:0.775245:0.874327:0.765128:0.874327:0.000000
):@0.800836:0.895915:0.806972:0.895915:0.806972:0.866232:0.800836:0.866232:0.000000
Onda de sonido de radio.:@0.092138:0.891179:0.243737:0.891179:0.243737:0.877770:0.092138:0.877770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.076640:0.832551:0.076640:0.827444:0.064559:0.827444:0.064559:0.832551:0.000000
Shutterstock:@0.076640:0.827444:0.076640:0.789725:0.064729:0.789725:0.064729:0.827444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática :@0.158711:0.484877:0.247750:0.484877:0.247750:0.469513:0.158711:0.469513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y tecnología:@0.155378:0.499964:0.244281:0.499964:0.244281:0.484600:0.155378:0.484600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Varias frecuencias de :@0.106059:0.518610:0.247950:0.518610:0.247950:0.503711:0.106059:0.503711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ondas de radio se usan :@0.091333:0.533698:0.247951:0.533698:0.247951:0.518799:0.091333:0.518799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para la televisión y :@0.121689:0.548785:0.247950:0.548785:0.247950:0.533886:0.121689:0.533886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
emisiones de radio FM :@0.094164:0.563873:0.247950:0.563873:0.247950:0.548974:0.094164:0.548974:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y AM, comunicaciones :@0.094131:0.578961:0.247951:0.578961:0.247951:0.564062:0.094131:0.564062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
militares, teléfonos :@0.119628:0.594048:0.247950:0.594048:0.247950:0.579149:0.119628:0.579149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
celulares, redes :@0.143182:0.609136:0.247950:0.609136:0.247950:0.594237:0.143182:0.594237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inalámbricas de :@0.139279:0.624224:0.247950:0.624224:0.247950:0.609325:0.139279:0.609325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
computadoras y otras :@0.098838:0.639311:0.247951:0.639311:0.247951:0.624412:0.098838:0.624412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
numerosas aplicaciones :@0.084900:0.654399:0.247951:0.654399:0.247951:0.639500:0.084900:0.639500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de comunicaciones.:@0.110850:0.669486:0.244281:0.669486:0.244281:0.654587:0.110850:0.654587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.089654:0.455718:0.246860:0.455718:0.246860:0.438817:0.089654:0.438817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.1.33. :@0.290067:0.965521:0.338404:0.965521:0.338404:0.954766:0.290067:0.954766:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconocer y calcular productos notables e identificar factores de expresiones algebraicas.:@0.338404:0.965521:0.755012:0.965521:0.755012:0.955091:0.338404:0.955091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.568842:0.965521:0.571410:0.965521:0.571410:0.955091:0.568842:0.955091:0.000000