74:@0.067867:0.963104:0.095634:0.963104:0.095634:0.941283:0.067867:0.941283:0.000000:0.000000
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
Productos notables I:@0.286308:0.079033:0.642450:0.079033:0.642450:0.042159:0.286308:0.042159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.094760:0.108604:0.159692:0.108604:0.159692:0.011516:0.094760:0.011516:0.000000
Los productos notables son ciertas multiplicaciones de polinomios que se utilizan :@0.287495:0.165449:0.907066:0.165449:0.907066:0.149061:0.287495:0.149061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para simplificar y reducir expresiones algebraicas, las cuales son llamadas notables :@0.287495:0.182046:0.907180:0.182046:0.907180:0.165657:0.287495:0.165657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
debido a su frecuente aparición y uso en problemas matemáticos y algebraicos. :@0.287495:0.198642:0.907086:0.198642:0.907086:0.182253:0.287495:0.182253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pueden ser escritos por simple inspección, es decir, sin realizar la multiplicación.:@0.287495:0.215239:0.869304:0.215239:0.869304:0.198850:0.287495:0.198850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los productos notables facilitan el proceso de multiplicación mediante reglas :@0.287495:0.238958:0.907141:0.238958:0.907141:0.222569:0.287495:0.222569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
específicas dadas.:@0.287495:0.255554:0.417316:0.255554:0.417316:0.239165:0.287495:0.239165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Veamos algunos productos notables.:@0.287495:0.279273:0.558544:0.279273:0.558544:0.262884:0.287495:0.262884:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Cuadrado de un binomio :@0.287495:0.319170:0.544099:0.319170:0.544099:0.297660:0.287495:0.297660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el diseño de un circuito impreso se ha tomado en consideración usar una placa :@0.287495:0.349078:0.907198:0.349078:0.907198:0.332689:0.287495:0.332689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de forma cuadrangular, de la cual se sabe a ciencia cierta que se dejará un margen :@0.287495:0.365675:0.907088:0.365675:0.907088:0.349286:0.287495:0.349286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de 5 :@0.287495:0.382271:0.325493:0.382271:0.325493:0.365882:0.287495:0.365882:0.000000:0.000000:0.000000:0.000000:0.000000
mm:@0.327465:0.382271:0.356728:0.382271:0.356728:0.365910:0.327465:0.365910:0.000000:0.000000
, tanto en la parte inferior como del lado derecho. De ese margen hacia :@0.356728:0.382271:0.907086:0.382271:0.907086:0.365882:0.356728:0.365882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adentro se podrán colocar pistas de cobre y los componentes electrónicos :@0.287495:0.398867:0.907123:0.398867:0.907123:0.382479:0.287495:0.382479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
necesarios. ¿Cuál es la expresión algebraica que representa el área de esa placa?:@0.287495:0.415464:0.870907:0.415464:0.870907:0.399075:0.287495:0.399075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Elaboramos un esquema de la forma de la placa y colocamos las medidas :@0.287495:0.439183:0.907180:0.439183:0.907180:0.422794:0.287495:0.422794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proporcionadas como datos. Al valor desconocido le asignamos la letra x.:@0.287495:0.455779:0.823734:0.455779:0.823734:0.439390:0.287495:0.439390:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otra forma de obtener el área de la placa es dividiéndola en cuatro áreas.:@0.287495:0.621854:0.820640:0.621854:0.820640:0.605465:0.287495:0.605465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Como se trata de la misma placa, podemos decir que::@0.287495:0.811647:0.680115:0.811647:0.680115:0.795258:0.287495:0.795258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.299778:0.836632:0.307684:0.836632:0.312488:0.820243:0.304582:0.820243:0.000000
x:@0.360718:0.836632:0.368624:0.836632:0.373428:0.820243:0.365523:0.820243:0.000000
x:@0.409404:0.836632:0.417310:0.836632:0.422114:0.820243:0.414208:0.820243:0.000000
(:@0.294719:0.836632:0.299602:0.836632:0.299602:0.820243:0.294719:0.820243:0.000000
5):@0.325033:0.836632:0.339019:0.836632:0.339019:0.820243:0.325033:0.820243:0.000000:0.000000
10:@0.392091:0.836632:0.409880:0.836632:0.409880:0.820243:0.392091:0.820243:0.000000:0.000000
25:@0.434647:0.836632:0.452441:0.836632:0.452441:0.820243:0.434647:0.820243:0.000000:0.000000
2:@0.339009:0.828971:0.344221:0.828971:0.344221:0.819473:0.339009:0.819473:0.000000
2:@0.372362:0.828971:0.377573:0.828971:0.377573:0.819473:0.372362:0.819473:0.000000
+:@0.312885:0.837310:0.323002:0.837310:0.323002:0.821737:0.312885:0.821737:0.000000
=:@0.348690:0.837310:0.358807:0.837310:0.358807:0.821737:0.348690:0.821737:0.000000
+:@0.381104:0.837310:0.391221:0.837310:0.391221:0.821737:0.381104:0.821737:0.000000
+:@0.422511:0.837310:0.432628:0.837310:0.432628:0.821737:0.422511:0.821737:0.000000
Al analizar los dos lados de la igualdad, podemos concluir que en el segundo :@0.287495:0.865385:0.907086:0.865385:0.907086:0.848996:0.287495:0.848996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
miembro tenemos el cuadrado del primer término, más el doble producto del :@0.287495:0.881982:0.907086:0.881982:0.907086:0.865593:0.287495:0.865593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
primer término con el segundo y el cuadrado del segundo término.:@0.287495:0.898578:0.782440:0.898578:0.782440:0.882189:0.287495:0.882189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática :@0.159341:0.664682:0.248380:0.664682:0.248380:0.649318:0.159341:0.649318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y robótica:@0.172358:0.679770:0.244913:0.679770:0.244913:0.664406:0.172358:0.664406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A fin de que un robot :@0.101680:0.698416:0.248580:0.698416:0.248580:0.683517:0.101680:0.683517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
realice las funciones para :@0.078461:0.713503:0.248581:0.713503:0.248581:0.698604:0.078461:0.698604:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las que fue creado, :@0.120392:0.728591:0.248580:0.728591:0.248580:0.713692:0.120392:0.713692:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
debe contar con un :@0.112971:0.743678:0.248581:0.743678:0.248581:0.728779:0.112971:0.728779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
circuito de control.:@0.120258:0.758766:0.244911:0.758766:0.244911:0.743867:0.120258:0.743867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esos circuitos de control :@0.083855:0.777412:0.248580:0.777412:0.248580:0.762513:0.083855:0.762513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se diseñan y luego son :@0.093203:0.792499:0.248581:0.792499:0.248581:0.777600:0.093203:0.777600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elaborados en placas de :@0.083570:0.807587:0.248581:0.807587:0.248581:0.792688:0.083570:0.792688:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
circuito impreso, donde :@0.086619:0.822675:0.248580:0.822675:0.248580:0.807776:0.086619:0.807776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se colocan los elementos :@0.077053:0.837762:0.248578:0.837762:0.248578:0.822863:0.077053:0.822863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
electrónicos. Estas placas :@0.078611:0.852850:0.248580:0.852850:0.248580:0.837951:0.078611:0.837951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son hechas a base de :@0.102618:0.867938:0.248581:0.867938:0.248581:0.853038:0.102618:0.853038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cobre, para la conducción, :@0.069465:0.883025:0.248581:0.883025:0.248581:0.868126:0.069465:0.868126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y de un material aislante, :@0.080069:0.898113:0.248578:0.898113:0.248578:0.883214:0.080069:0.883214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como la baquelita. :@0.121699:0.913200:0.248581:0.913200:0.248581:0.898301:0.121699:0.898301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Interdisciplinariedad:@0.090285:0.635523:0.247491:0.635523:0.247491:0.618622:0.090285:0.618622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Memorias de computador:@0.101810:0.570689:0.259005:0.570689:0.259005:0.557280:0.101810:0.557280:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©:@0.066974:0.482609:0.066974:0.477502:0.054893:0.477502:0.054893:0.482609:0.000000
Shutterstock:@0.066974:0.477502:0.066974:0.439783:0.055063:0.439783:0.055063:0.477502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El gráfico nos muestra un cuadrado :@0.594555:0.499213:0.878654:0.499213:0.878654:0.482824:0.594555:0.482824:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuyo lado mide x + 5. Por lo tanto, su :@0.594555:0.515809:0.878654:0.515809:0.878654:0.499420:0.594555:0.499420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
área es::@0.594555:0.532405:0.648511:0.532405:0.648511:0.516016:0.594555:0.516016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.611251:0.559554:0.621367:0.559554:0.621367:0.543981:0.611251:0.543981:0.000000
+:@0.642762:0.559554:0.652879:0.559554:0.652879:0.543981:0.642762:0.543981:0.000000
+:@0.687891:0.559554:0.698008:0.559554:0.698008:0.543981:0.687891:0.543981:0.000000
=:@0.611256:0.582147:0.621372:0.582147:0.621372:0.566574:0.611256:0.566574:0.000000
+:@0.642767:0.582147:0.652884:0.582147:0.652884:0.566574:0.642767:0.566574:0.000000
A:@0.598633:0.558870:0.608528:0.558870:0.608528:0.542509:0.598633:0.542509:0.000000
x:@0.631397:0.558870:0.638860:0.558870:0.638860:0.542509:0.631397:0.542509:0.000000
x:@0.676526:0.558870:0.683989:0.558870:0.683989:0.542509:0.676526:0.542509:0.000000
A:@0.598639:0.581469:0.608535:0.581469:0.608535:0.565108:0.598639:0.565108:0.000000
x:@0.631404:0.581469:0.638867:0.581469:0.638867:0.565108:0.631404:0.565108:0.000000
(:@0.624239:0.558877:0.629122:0.558877:0.629122:0.542488:0.624239:0.542488:0.000000
5)(:@0.655658:0.558877:0.674251:0.558877:0.674251:0.542488:0.655658:0.542488:0.000000:0.000000:0.000000
5):@0.700787:0.558877:0.714774:0.558877:0.714774:0.542488:0.700787:0.542488:0.000000:0.000000
(:@0.624239:0.581469:0.629122:0.581469:0.629122:0.565080:0.624239:0.565080:0.000000
5):@0.655658:0.581469:0.669644:0.581469:0.669644:0.565080:0.655658:0.565080:0.000000:0.000000
2:@0.669628:0.573807:0.674839:0.573807:0.674839:0.564309:0.669628:0.564309:0.000000
x:@0.418201:0.497920:0.425664:0.497920:0.425664:0.481559:0.418201:0.481559:0.000000
x:@0.371948:0.524474:0.379411:0.524474:0.379411:0.508113:0.371948:0.508113:0.000000
5:@0.371948:0.564209:0.380461:0.564209:0.380461:0.547848:0.371948:0.547848:0.000000
5:@0.460953:0.497450:0.469467:0.497450:0.469467:0.481089:0.460953:0.481089:0.000000
Obtenemos el área total al sumar :@0.600295:0.656916:0.880341:0.656916:0.880341:0.640527:0.600295:0.640527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
las cuatro áreas.:@0.600295:0.673512:0.715392:0.673512:0.715392:0.657123:0.600295:0.657123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.616993:0.699171:0.627110:0.699171:0.627110:0.683598:0.616993:0.683598:0.000000
+:@0.650495:0.699171:0.660612:0.699171:0.660612:0.683598:0.650495:0.683598:0.000000
+:@0.684567:0.699171:0.694684:0.699171:0.694684:0.683598:0.684567:0.683598:0.000000
+:@0.718640:0.699171:0.728757:0.699171:0.728757:0.683598:0.718640:0.683598:0.000000
Ax:@0.604370:0.698494:0.639328:0.698494:0.639328:0.682132:0.604370:0.682132:0.000000:0.000000
x:@0.673216:0.698494:0.680679:0.698494:0.680679:0.682132:0.673216:0.682132:0.000000
x:@0.707289:0.698494:0.714752:0.698494:0.714752:0.682132:0.707289:0.682132:0.000000
5:@0.663376:0.698494:0.672368:0.698494:0.672368:0.682105:0.663376:0.682105:0.000000
5:@0.697448:0.698494:0.706441:0.698494:0.706441:0.682105:0.697448:0.682105:0.000000
5:@0.731521:0.698494:0.740514:0.698494:0.740514:0.682105:0.731521:0.682105:0.000000
2:@0.640971:0.690832:0.646183:0.690832:0.646183:0.681334:0.640971:0.681334:0.000000
2:@0.740228:0.690832:0.745439:0.690832:0.745439:0.681334:0.740228:0.681334:0.000000
Reduciendo términos semejantes, :@0.600295:0.724732:0.880319:0.724732:0.880319:0.708343:0.600295:0.708343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tenemos::@0.600295:0.741329:0.668606:0.741329:0.668606:0.724940:0.600295:0.724940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.616993:0.766989:0.627110:0.766989:0.627110:0.751416:0.616993:0.751416:0.000000
+:@0.650495:0.766989:0.660612:0.766989:0.660612:0.751416:0.650495:0.751416:0.000000
+:@0.693007:0.766989:0.703124:0.766989:0.703124:0.751416:0.693007:0.751416:0.000000
Ax:@0.604370:0.766311:0.639328:0.766311:0.639328:0.749950:0.604370:0.749950:0.000000:0.000000
x:@0.681637:0.766311:0.689101:0.766311:0.689101:0.749950:0.681637:0.749950:0.000000
10:@0.662215:0.766311:0.679997:0.766311:0.679997:0.749922:0.662215:0.749922:0.000000:0.000000
25:@0.705870:0.766311:0.723652:0.766311:0.723652:0.749922:0.705870:0.749922:0.000000:0.000000
2:@0.640971:0.758649:0.646183:0.758649:0.646183:0.749151:0.640971:0.749151:0.000000
x:@0.419861:0.671460:0.427324:0.671460:0.427324:0.655099:0.419861:0.655099:0.000000
x:@0.373608:0.698015:0.381071:0.698015:0.381071:0.681653:0.373608:0.681653:0.000000
5:@0.373608:0.737749:0.382121:0.737749:0.382121:0.721388:0.373608:0.721388:0.000000
5:@0.462613:0.670990:0.471127:0.670990:0.471127:0.654629:0.462613:0.654629:0.000000
x2:@0.414522:0.704556:0.427016:0.704556:0.427016:0.688195:0.414522:0.688195:0.000000:0.000000
5x:@0.414522:0.738358:0.430499:0.738358:0.430499:0.721996:0.414522:0.721996:0.000000:0.000000
5x:@0.458454:0.704556:0.474430:0.704556:0.474430:0.688195:0.458454:0.688195:0.000000:0.000000
25:@0.459635:0.738887:0.475817:0.738887:0.475817:0.723988:0.459635:0.723988:0.000000:0.000000
La matemática :@0.146532:0.210808:0.248588:0.210808:0.248588:0.195909:0.146532:0.195909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es fundamental para :@0.107667:0.225895:0.248588:0.225895:0.248588:0.210996:0.107667:0.210996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la gente que vive en el :@0.094466:0.240983:0.248586:0.240983:0.248586:0.226084:0.094466:0.226084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
campo, pues les ayuda a :@0.082136:0.256071:0.248586:0.256071:0.248586:0.241172:0.082136:0.241172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
medir sus terrenos, :@0.118774:0.271158:0.248586:0.271158:0.248586:0.256259:0.118774:0.256259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dividirlos en parcelas; para :@0.069790:0.286246:0.248586:0.286246:0.248586:0.271347:0.069790:0.271347:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sus plantaciones; para :@0.098470:0.301334:0.248588:0.301334:0.248588:0.286435:0.098470:0.286435:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
establecer la cantidad de :@0.078333:0.316421:0.248588:0.316421:0.248588:0.301522:0.078333:0.301522:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
semillas que necesitan, los :@0.069421:0.331509:0.248588:0.331509:0.248588:0.316610:0.069421:0.316610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
productos que venden, :@0.088971:0.346596:0.248586:0.346596:0.248586:0.331697:0.088971:0.331697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre otros.:@0.169349:0.361684:0.244919:0.361684:0.244919:0.346785:0.169349:0.346785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Educación :@0.142567:0.171168:0.224251:0.171168:0.224251:0.154267:0.142567:0.154267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
financiera:@0.145753:0.184998:0.220802:0.184998:0.220802:0.168097:0.145753:0.168097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.150646:0.184998:0.154270:0.184998:0.154270:0.168097:0.150646:0.168097:0.000000
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