分解因式2a+2a^2+4a^3(x+y)^2-2x-2y+1(x^2+y^2-1)^2-4x^2y^2^2是平方^3是三次方

Question

分解因式
2a+2a^2+4a^3
(x+y)^2-2x-2y+1
(x^2+y^2-1)^2-4x^2y^2
^2 是平方
^3是三次方

Answer 1

2a+2a^2+4a^3
=2a(2a²+a+1)
(x+y)^2-2x-2y+1
=(x+y)²-2(x+y)+1
=(x+y-1)²
(x^2+y^2-1)^2-4x^2y^2
=(x²+y²-1+2xy)(x²+y²-1-2xy）
=[(x+y)²-1)][(x-y)²-1]
=(x+y+1)(x+y-1)(x-y+1)(x-y-1)