因式分解 9-x²-b²+2xy 和 x⁴+x²y²+y⁴_数学解答

因式分解 9-x²-b²+2xy 和 x⁴+x²y²+y⁴

人气：194 ℃　时间：2020-03-13 20:27:17

解答

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)