Question

再问一题分解因式2x^2+xy-y^2-4x+5y-6

Answer 1

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)
=(x+y-3)(2x-y+2)

追问

2x^2+xy-y^2=(2x-y)(x+y)是怎么得到的啊，我秀逗了

追答

因式分解啊（十字相错法）
2x -y
x +y

Answer 2

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