题目

因式分解：x-xy²；-36m²+4n²；x的4次方-16；81（x+y）4次方-16（x-y）4次方

提问时间：2020-05-19

答案

x-xy²
=-x(y²-1)
=-x(y+1)(y-1)
-36m²+4n²；
=4(n²-9m²)
=4(n+3m)(n-3m)
x的4次方-16
=(x²+4)(x²-4)
=(x²+4)(x+2)(x-2)
81（x+y）4次方-16（x-y）4次方
=[9(x+y)²+4(x-y)²][9(x+y)²-4(x-y)²]
=(9x²+18xy+9y²+4x²-8xy+4y²)[3(x+y)+2(x-y)][3(x+y)-2(x-y)]
=(13x²+10xy+13y²)(5x+y)(x+5y)