Question

2x2+xy-y2-4x+5y-6用分组分解法来因式分解（x或y后的二是表平方）

Answer 1

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)

Answer 2

2x^2+xy-y^2-4x+5y-62x^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)