Question

Разложите на множители выражение (x+y)^2-x^4-y^4+2x^2y^2

Answer 1

$(x+y)^2-x^4-y^4+2x^2y^2=(x+y)^2-(x^4+y^4-2x^2y^2)=$$=(x+y)^2-(x^2-y^2)^2=(x+y)^2-((x-y)(x+y))^2=$$=(x+y-(x-y)(x+y))(x+y+(x-y)(x+y))=$$(x+y)(1-x+y)(x+y)(1+x-y)=(x+y)^2(1-x+y)(1+x-y)$

$a^2-b^2=(a-b)(a+b)$