Question

2x²+xy-y²-4x+5y-6怎么用分组分解法分解因式，带着过程，求解答

Answer 1

麻烦点击分类右侧的那个小笔按钮把分类修改成数学，谢谢

解：

2x²+xy-y²-4x+5y-6

=(2x²+xy-y²)+(-4x+5y)-6   分组

=(2x-y)(x+y)-4x+5y-6      第一组内利用十字相乘法
=(2x-y)(x+y)+(2x+2y)-6x+3y-6    继续分组
=(2x-y)(x+y)+2(x+y)-6x+3y-6    
=(x+y)(2x-y+2)-3(2x-y+2)   提取公因式
=(x+y-3)(2x-y+2)    提取公因式

Answer 2

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