因式分解2x^2+xy-y^2-4x+5y-6

2022-08-04 23:40

4个回答

2022-08-05 02:29

2x^2+xy-y^2-4x+5y-6
=(2x-y)(x+y)-4x+5y-6
=(2x-y)(x+y)+(2x+2y)-6x+3y-6
=(2x-y)(x+y)+2(x+y)-6x+3y-6
=(x+y)(2x-y+2)-3(2x-y+2)
=(2x-y+2)(x+y-3)

2022-08-05 02:27

一共有三种解法
用十字相乘法法，把y作为常数，x 做降幂排列。
原式=2x2+(y-4)x+(-y2+5y-6)
=2x2+(y-4)x+[-(y2-5y+6)]
=2x2+(y-4)x+[-(y-2)(y-3)]
作十字分解，如下：
1 y-3
2 -y+2
则：
原式=[1x+(y-3)][2x+(-y+2)]
=(x+y-3)(2x-y+2)
验算，结果=2x2-xy+2x+2xy-y2+2y-6x+3y-6
=2x2+xy-y2+5y-6=题目的式子无误
将2x^2+xy-y^2因式分解：2x^2+xy-y^2＝(2x-y)(x+y)
那么假设2x^2+xy-y^2-4x+5y-6可以分解为(2x-y+a)(x+y+b)
展开：2x^2+xy-y^2+(a+2b)x+(a-b)y+ab
那么：a+2b=-4, a-b=5, ab=-6
解出a＝2，b＝－3
所以：2x^2+xy-y^2-4x+5y-6＝(2x-y+2)(x+y-3)

2x^2+xy-y^2-4x+5y-6
=(2x-y)(x+y)-4x+5y-6
=(2x-y)(x+y)+(2x+2y)-6x+3y-6
=(2x-y)(x+y)+2(x+y)-6x+3y-6
=(x+y)(2x-y+2)-3(2x-y+2)
=(2x-y+2)(x+y-3)

2022-08-05 00:13

将2x^2+xy-y^2因式分解：2x^2+xy-y^2＝(2x-y)(x+y)
那么假设2x^2+xy-y^2-4x+5y-6可以分解为(2x-y+a)(x+y+b)
展开：2x^2+xy-y^2+(a+2b)x+(a-b)y+ab
那么：a+2b=-4, a-b=5, ab=-6
解出a＝2，b＝－3
所以：2x^2+xy-y^2-4x+5y-6＝(2x-y+2)(x+y-3)

2022-08-05 00:10

用十字相乘法法，把y作为常数，x 做降幂排列。
原式=2x2+(y-4)x+(-y2+5y-6)
=2x2+(y-4)x+[-(y2-5y+6)]
=2x2+(y-4)x+[-(y-2)(y-3)]
作十字分解，如下：
1 y-3
2 -y+2
则：
原式=[1x+(y-3)][2x+(-y+2)]
=(x+y-3)(2x-y+2)
验算，结果=2x2-xy+2x+2xy-y2+2y-6x+3y-6
=2x2+xy-y2+5y-6=题目的式子无误