Question

(x+y)^2 (x-y)^2 ¿cómo lo convierto en un polinomio?

Answer 1

Respuesta:

$x^{4}-2x^{2}y^{2}+ y^{4}$

Explicación paso a paso:

$Primera\ manera\ de\ resolver:\\ (x+y)^{2}(x-y)^{2}= (x^{2} +2xy+y^{2})(x^{2}-2xy+y^{2})\\\\\Rightarrow (x^{4}-2x^{3}y+x^{2}y^{2})+(2x^{3}y-4x^{2}y^{2}+2xy^{3})+(x^{2}y^{2}-2xy^{3}+y^{4})\\\\\Rightarrow x^{4}-2x^{3}y+x^{2}y^{2}+2x^{3}y-4x^{2}y^{2}+2xy^{3}+x^{2}y^{2}-2xy^{3}+y^{4}\\\\\Rightarrow x^{4}-2x^{2}y^{2}+ y^{4}$

$Segunda\ manera\ de\ resolver:\ \\ (x+y)^{2}(x-y)^{2}= ((x+y)(x-y))^{2}, propiedad\ (a+b)(a-b)= a^{2}- b^{2}\\\\ luego,\ ((x+y)(x-y))^{2}=(x^{2} -y^{2})^{2} \Rightarrow [(x^{2})^{2}-2(x^{2} -y^{2})+(y^{2})^{2}]\\\\ \Rightarrow x^{4}-2x^{2}y^{2}+ y^{4}$