因式分解题 (19 20:23:15)

题目

因式分解题 (19 20:23:15)
1.   (x+y) ²(x-y)+(x+y)(x-y)²
2.   2a(a-3)²-6a²(3-a)+8a(a-3)
3.   24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)

答案

1. (x+y) ²(x-y)+(x+y)(x-y)²
= (x+y) (x-y)(x+y+x-y)
=2x(x+y) (x-y)
2. 2a(a-3)²-6a²(3-a)+8a(a-3)
=2a(a-3)²+6a²(a-3)+8a(a-3)
=2a(a-3)(a-3+3a+4)
=2a(a-3)(4a+1)
3. 24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)
=24xy²z²(x+y-z)+32xyz(x+y-z)²-8xyz³(x+y-z)
=8xyz(x+y-z)[3yz+4(x+y-z)-z^2]