因式分解 9-x²-b²+2xy 和 x⁴+x²y²+y⁴

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因式分解 9-x²-b²+2xy 和 x⁴+x²y²+y⁴
因式分解 9-x²-b²+2xy 和 x⁴+x²y²+y⁴

因式分解 9-x²-b²+2xy 和 x⁴+x²y²+y⁴
9-x²-y²+2xy
=9-(x²-2xy+y²)
=9-(x-y)²
=[3+(x-y)][3-(x-y)]
=(3+x-y)(3-x+y)
x⁴+x²y²+y⁴
=x⁴+2x²y²+y⁴-x²y²
=(x²+y²)²-(xy)²
=(x²+y²+xy)(x²+y²-xy)

9-x²-y²+2xy
= 9-(x²+y²-2xy)
= 9-(x-y)²
=(3-x+y)(3+x-y)
x⁴+x²y²+y⁴
=x⁴+2x²y²+y⁴-x²y²
=(x²+y²)²-x²y²
=(x²+y²-xy)(x²+y²+xy)