因式分解 (x2-y2)2-8(x2+y2-2)

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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+y²-2)
=(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)

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