题目

急
a²-ab+ac-bc
2ax-10ay+5by-bx
3ax+4by+4ay+3bx
m²+5m-mn-5n
x²-y²+ax+ay
a²-2ab+b²-c²
x³+x²y-xy²-y³
4a²-b²+6a-3b
9m²-6m+2n-n²
x²-y²-z²+2yz
x³-x²y-xy²+y³

提问时间：2021-03-14

答案

WYZYKJCWYXCX ：
a²-ab+ac-bc
=a(a-b)+c(a-b)
=(a+c)(a-b)
2ax-10ay+5by-bx
=x(2a-b)-5y(2a-b)
=(x-5y)(2a-b)
3ax+4by+4ay+3bx
=3x(a+b)+4y(a+b)
=(a+b)(3x+4y)
m²+5m-mn-5n
=m(m+5)-n(m+5)
=(m+5)(m-n)
x²-y²+ax+ay
=(x+y)(x-y)+a(x+y)
=(x+y)(x-y+a)
a²-2ab+b²-c²
=(a-b)²-c²
=(a-b+c)(a-b-c)
x³+x²y-xy²-y³
=x²(x+y)-y²(x+y)
=(x²-y²)(x+y)
=(x+y)(x-y)(x+y)
=(x+y)²(x-y)
4a²-b²+6a-3b
=(2a+b)(2a-b)+3(2a-b)
=(2a-b)(2a+b+3)
9m²-6m+2n-n²
=9m²-n²-6m+2n
=(3m+n)(3m-n)-2(3m-n)
=(3m-n)(3m+n-2)
x²-y²-z²+2yz
=x²-(y²+z²-2yz)
=x²-(y-z)²
=(x+y-z)(x-y+z)
x³-x²y-xy²+y³
=x²(x-y)-y²(x-y)
=(x²-y²)(x-y)
=(x+y)(x-y)(x-y)
=(x+y)(x-y)²