2（2-X）方-X（X-2)立方（因式分解）

2(2-X)^2-X(X-2)^3
=2(X-2)^2-X(X-2)^3
=(X-2)^2[2-X(X-2)]
=(X-2)^2(2-X^2+2X)
=-(X-2)^2(X^2-2X-2)

1.
（X-1)(X-2)-2(2-X)^2
=(X-1)(X-2)-2(X-2)^2
=(X-2)[(X-1)-2(X-2)]
=(X-2)(X-1-2X+4)
=(X-2)(3-X)
=-(X-2)(X-3)

2.
（X^2+X+1)(X^2+X+2)-12
=(X^2+X)^2+3(X^2+X)+2-12
=(X^2+X)^2+3(X^2+X)-10
=[(X^2+X)-2][(X^2+X)+5]
=(X^2+X-2)(X^2+X+5)
=(X+2)(X-1)(X^2+X+5)

3.
（X-Y)(3X+Y)^2+(X+3Y)^2(Y-X)
=(X-Y)(3X+Y)^2-(X+3Y)^2(X-Y)
=(X-Y)[(3X+Y)^2-(X+3Y)^2]
=(X-Y)[(3X+Y)-(X+3Y)][(3X+Y)+(X+3Y)]
=(X-Y)(3X+Y-X-3Y)(3X+Y+X+3Y)
=(X-Y)(2X-2Y)(4X+4Y)
=2(X-Y)(X-Y)(4X+4Y)
=8(X-Y)(X-Y)(X+Y)
=8(X-Y)^2(X+Y)

4.
2X^2(X-Y)+2Y^2(Y-X)
=2X^2(X-Y)-2Y^2(X-Y)
=2(X-Y)(X^2-Y^2)
=2(X-Y)(X-Y)(X+Y)
=2(X-Y)^2(X+Y)

1.原式=[（x-1)-2(x-2)](x-2)
= -(x+3)(x-2)
2.设x方+x+1=a
原式=a（a+1)-12
=a方+a-12
=(a+4)(a-3)
=(x方+x+5)(x方+