Question

2x²+xy-y²-4x_5y

方法：分组分解法,例：2x²+xy-y²-4x+5y-6 原式=2x²+(y-4)x-y²+5y-6
=(2x²+xy-y²)-(4x-5y)-6 或 =2x²+(y-4)x-(y-2)(y-3)
=(2x-y)(x+y)-(4x-5y)-6 =(2x-y+2)(x+y-3)
=(2x-y+2)(x+y-3)
用分组分解法分解多项式（1）x²-y²+a²-b²+2ax+2bx
(2) a²-4ab+4b²-6a+12b+9

Answer 1

1）原式=(x^2+2ax+a^2)-(y^2-2bx+b^2)
=(x+a)^2-(y-b)^2
=(x+a+y-b)(x+a-y+b)

2) 原式=(a-2b)^2-6(a-2b)+9
=(a-2b-3)^2