1.（x+y）²-(x+y)³2.（x-y)²-（x-y)³3.(x-y)²-（y-x)³4.2（x-y)-3（y-x)²5.4ab(a+b)²-6a²b(a+b)6.(x+y)²（x-y)+（x+y)（x-y)²7.2a(a-3)²-6a²（3-a）+8a(a-3)8.24xy²z²（x+y-z

Question

1.（x+y）²-(x+y)³
2.（x-y)²-（x-y)³
3.(x-y)²-（y-x)³
4.2（x-y)-3（y-x)²
5.4ab(a+b)²-6a²b(a+b)
6.(x+y)²（x-y)+（x+y)（x-y)²
7.2a(a-3)²-6a²（3-a）+8a(a-3)
8.24xy²z²（x+y-z)-32xyz(z-x-y)²+8xyz³（z-x-y)

Answer 1

解1题
原式=(x+y)²-(x+y)³
=(x+y)²[1-(x+y)]
=(x+y)²(1-x-y)
2题
原式=(x-y)²-(x-y)³
=(x-y)²[1-(x-y)]
=(x-y)²(1-x+y)
3题
原式=(x-y)²-(y-x)³
=(x-y)²+(x-y)³
=(x-y)²[1+(x-y)]
=(x-y)²(1+x-y)
4题
原式=2(x-y)-3(y-x)²
=2(x-y)-3(x-y)²
=(x-y)[2-3(x-y)]
=(x-y)(2-3x+3y)
5题
原式=4ab(a+b)²-6a²b(a+b)
=2ab(a+b)[2(a+b)-3a]
=2ab(a+b)(2a+2b-3a)
=2ab(a+b)(2b-a)
6题
原式=(x+y)²(x-y)+(x+y)(x-y)²
=(x+y)(x-y)[(x+y)+(x-y)]
=(x+y)(x-y)(x+y+x-y)
=2x(x+y)(x-y)
7题
原式=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)(a-3+3a+4)
=2a(a-3)(4a+1)
8题
原式=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)-z²]
=8xyz(x+y-z)(3yz-4x-4y+4z-z²)