x^2-2xy-8y^2=(x+2y)(x-4y)假设a(x+2y)+b(x-4y)=-2x+14y则a+b=-2,2a-4b=14解得:a=1,b=-3那么x^2-2xy-8y^2-2x+14y-3=(x+2y)(x-4y)+(x+2y)-3(x-4y)-3=(x+2y)(x-4y+1)-3(x-4y+1)=(x+2y-3)(x-4y+1)