几道因式分解的题,求解(急~)

来源:百度知道 编辑:UC知道 时间:2024/05/13 03:16:07
⑴x^2-8x+12
⑵a^2(x-y)+b^2(y-x)
⑶(y+1)(y^2-1)-(y+1)^3
⑷(x^2+y^2)^2-4x^2y^2

详细过程,(追加分)

1、=(x-2)(x-6)
2 =(x-y)(a+b)a-b)
3 =(y+1)[y^2-1-(y+1)^2]
=-2(y+1)(y+1)
4 =(x^2+y^2+2xy)(x^2+y^2-2xy)
=(x+y)^2(x-y)^2

⑴x^2-8x+12=x^2-(2+6)x+2*6=(x-2)(x-6)
⑵a^2(x-y)+b^2(y-x)= a^2(x-y)-b^2(x-y)=(x-y)( a^2-b^2)=
(x-y)(a+b)(a-b)
⑶(y+1)(y^2-1)-(y+1)^3=(y+1)( y+1)(y-1)-(y+1)^3=(y+1)^2(y-1)-(y+1)^3=(y+1)^2[(y-1)-(y+1)]=(y+1)^2(-2)=-2(y+1)^2
⑷(x^2+y^2)^2-4x^2y^2 =(x^2+y^2)^2-(2xy)^2=(x^2+y^2+2xy)(x^2+y^2-2xy)
祝学习进步!