江苏银行杭州萧山支行:因式分解

来源:百度文库 编辑:高校问答 时间:2024/03/29 20:02:24
1.(x-y)(2x-y)-(x-2y)(y-x)

2.x(x^2-6)^2-4x^2(x^2-6)-5x^3

3.(x^2+5x+6)(x^2+7x+6)-3x^2

4.y^2(x+1)^2-x^2-2xy^2-y^4

1)(x+y)(2x-y)-(x-2y)(y-x)
=(2x^2+xy-y^2)-(-x^2+3xy-2y^2)
=3x^2-2xy+y^2
=2x^2+(x-y)^2。在实数范围内不能分解。
2)x(x^2-6)^2-4x^2*(x^2-6)-5x^3 (x^2 ?)
=x[(x^2-6)^2-4x(x^2-6)-5x^2]
=x[(x^2-6)+x]*[(x^2-6)-5x]
=x(x^2+x-6)(x^2-5x-6)
=x(x+3)(x-2)(x+1)(x-6)
3)(x^2+5x+6)(x^2+7x+6)-3x^2
=[(x^2+6)+5x]*[(x^2+6)+7x]-3x^2
=(x^2+6)^2+12x(x^2+6)+35x^2-3x^2
=(x^2+6)^2+12x(x^2+6)+32x^2
=(x^2+6+4x)(x^2+6+8x)
=(x+2)(x+4)(x^2+4x+6)
4)y^2*(x+1)^2-x^2-2xy^2-y^4
=y^2*(x+1)^2-[x^2+2xy^2+(y^2)^2]
=[y(x+1)]^2-(x+y^2)^2
=(xy+y-x-y^2)(xy+y+x+y^2)
=[x(y-1)-y(y-1)][x(y+1)+y(y-1)]
=(y-1)(x-1)(y+1)(x+1)