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因式分解(x²-y²)²-8(x²+y²)+16

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因式分解(x²-y²)²-8(x²+y²)+16
因式分解(x²-y²)²-8(x²+y²)+16
(x²-y²)²-8(x²+y²)+16=(x²+y²)²-8(x²+y²)+16-4x²y²=(x²+y²-4)²-4x²y²=(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)