Question

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Answer 1

Answer:

$(x^2+y^2+xy)(x^2+y^2-xy)$

Step-by-step explanation:

Rewrite the middle term.

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

Rerrange terms.

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

Factor first three terms by perfect square rule.

$(x^2+y^2)^2-x^2y^2$

Rewrite $x^2y^2$ as $(xy)^2$.

$(x^2+y^2)^2-(xy)^2$

Since both terms are perfect squares, factor using the difference of squares formula, $a^2-b^2=(a+b)(a-b)$ where $a=x^2+y^2$ and $b=xy$.

$(x^2+y^2+xy)(x^2+y^2-(xy))$

Remove parentheses.

$(x^2+y^2+xy)(x^2+y^2-xy)$