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七年级数学解答题一般
题目
因式分解:z2(x−y)+4(y−x)+3z(x−y)z^{2}(x-y)+4\left(y-x\right)+3z\left(x-y\right).
知识点：分式的乘除法章节：未标注

答案与解析

答案

z2(x−y)+4(y−x)+3z(x−y)z^{2}(x-y)+4\left(y-x\right)+3z\left(x-y\right)
=z2(x−y)−4(x−y)+3z(x−y)=z^{2}(x-y)-4\left(x-y\right)+3z\left(x-y\right)
=(x−y)(z2−4+3z)=\left(x-y\right)(z^{2}-4+3z)
=(x−y)(z−1)(z+4)=\left(x-y\right)\left(z-1\right)\left(z+4\right).

解析

z2(x−y)+4(y−x)+3z(x−y)z^{2}(x-y)+4\left(y-x\right)+3z\left(x-y\right)
=z2(x−y)−4(x−y)+3z(x−y)=z^{2}(x-y)-4\left(x-y\right)+3z\left(x-y\right)
=(x−y)(z2−4+3z)=\left(x-y\right)(z^{2}-4+3z)
=(x−y)(z−1)(z+4)=\left(x-y\right)\left(z-1\right)\left(z+4\right).

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