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

Question

如题所述

Answer 1

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)来自：求助得到的回答

Answer 2

x-xy²
=x(1-y²)
=x(1+y)(1-y)

-36m²+4n²
=4n²-36m²
=4(n²-9m²)
=4(n+3m)(n-3m)

81(x+y)^4 -16(x-y)^4
=[9(x+y)²+4(x-y)²][9(x+y)²-4(x-y)²]
=(13x²+10xy+13y²)[3(x+y)+2(x-y)][3(x+y)-2(x-y)]
=(13x²+10xy+13y²)(5x+y)(x+5y)