(x²-y²)²-8(x²+y²-2)因式分解

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(x²-y²)²-8(x²+y²-2)因式分解
(x²-y²)²-8(x²+y²-2)因式分解

(x²-y²)²-8(x²+y²-2)因式分解
(x²-y²)²-8(x²+y²-2)
=(x²-y²)²-8(x²-y²+2y²-2)
=(x²-y²)²-8(x²-y²)+16-16y²
=(x²-y²-4)²-16y²
=(x²-y²-4+4y)*((x²-y²-4-4y)
=[x²-(y²-4y+4)]*[x²-(y²+4y+4)]
=[x²-(y-2)²]*[x²-(y+2)²]
=(x+y-2)(x-y+2)(x+y+2)(x-y-2)