Answer:
[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]
Step-by-step explanation:
Rewrite the middle term.
[tex]x^4+2x^2y^2-x^2y^2+y^4[/tex]
Rerrange terms.
[tex]x^4+2x^2y^2+y^4-x^2y^2[/tex]
Factor first three terms by perfect square rule.
[tex](x^2+y^2)^2-x^2y^2[/tex]
Rewrite [tex]x^2y^2[/tex] as [tex](xy)^2[/tex].
[tex](x^2+y^2)^2-(xy)^2[/tex]
Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x^2+y^2[/tex] and [tex]b=xy[/tex].
[tex](x^2+y^2+xy)(x^2+y^2-(xy))[/tex]
Remove parentheses.
[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]
