作业帮4x^2+xy-y^2-4x+5y-6因式分解
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/13 10:17:49
4x^2+xy-y^2-4x+5y-6因式分解
4x^2+xy-y^2-4x+5y-6因式分解
4x^2+xy-y^2-4x+5y-6因式分解
是不是:2x^2+xy-y^2-4x+5y-6因式分解
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)
方法二:
将2x^2+xy-y^2因式分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)
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