Question

2(y-x)^2+3(x-y) 分解因式

Answer 1

由于(y-x)²=（x-y）²
所以原式=2（x-y）²+3(x-y)=(x-y)[2（x-y）+3]

Answer 2

（x-y）【2（x-y）+3】

Answer 3

2(y-x)^2+3(x-y)
=2(x-y)^2+3(x-y)
=(x-y)[2(x-y)+3]
=(x-y)(2x-2y+3)

Answer 4

2(y-x)^2+3(x-y)
=2(x-y)^2+3(x-y)
=(x-y)[2(x-y)+3]
=(x-y)(2x-2y+3)

追问

2(x-y)^2+3(x-y)
=(y-x)(2y+2x-3)
这样算对不对?

追答

不对，=(y-x)(2y-2x-3)或者上面那个

追问

2(x-y)^2+3(x-y)
=2(x+y)(x-y)+3(x-y)
=(y-x){2(y+x)-3}
=(y-x)(2y+2x-3)
具体错在哪里？请帮我指出，灰常感谢！！
还有，在你的解法里，(x-y)^2=(y-x)^2 一定成立吗？

追答

2(x-y)^2=2(x-y)*(x-y)哦
(x^2-y^2)=(x+y)(x-y)

(x-y)^2=(y-x)^2是一定成立的

追问

不明白啊~~

追答

(x-y)²与(x²-y²)是不同的
(x-y)²是两个(x-y)相乘，就好比3²=3*3,(3-2)²=1²=(3-2)(3-2)=1而不是等于(3+2)(3-2)=6

追问

哎呀！晓得啦~~谢谢谢谢~~~~