(X+Y)^2(X-Y)+(X+Y)(X-Y)^2答案不是2xy(x+y)(x-y)24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz^3(z-x-y)这两题怎么做,要过程!
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问题描述：
(X+Y)^2(X-Y)+(X+Y)(X-Y)^2答案不是2xy(x+y)(x-y)
24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz^3(z-x-y)这两题怎么做,要过程!
杜永文回答：
(x+y)²(x-y)+(x+y)(x-y)²提取公因式(x+y)(x-y)
=(x+y)(x-y)[(x+y)+(x-y)]
=(x+y)(x-y)(x+y+x-y)
=2x(x+y)(x-y)
24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)
=24xy²z²(x+y-z)-32xyz[-1×(x+y-z)]²-8xyz³(x+y-z)
=24xy²z²(x+y-z)-32xyz×(-1)²×(x+y-z)²-8xyz³(x+y-z)
=24xy²z²(x+y-z)-32xyz(x+y-z)²-8xyz³(x+y-z)提取公因式8xyz(x+y-z)
=8xyz(x+y-z)[3yz-4(x+y-z)-z²]
=8xyz(x+y-z)(3yz-4x-4y+4z-z²)
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