Question

因式分解 (x2-y2)2-8(x2+y2-2)

Answer 1

(x²-y²)²-8(x²+y²-2)

=(x²+y²)²-4x²y²-8(x²+y²)+16

=(x²+y²)²-8(x²+y²)+16-(2xy)²

=(x²+y²-4)²-(2xy)²

=(x²+y²-4-2xy)(x²+y²-4+2xy)

=[(x-y)²-4][(x+y)²-4]

=(x-y-2)(x-y+2)(x+y-2)(x+y+2)