Đáp án `+` Giải thích các bước giải:

`1. (x-1)^3+3(x+1)^2=(x^2-2x+4)(x+2)`

`(x^3-3x^2+3x-1)+3(x^2-2x+1)=x^3+2^3`

`x^3-3x^2+3x-1+3x^2-6x+3=x^3+8`

`x^3-3x+2=x^3+8`

`-3x+2=8`

`-3x=8-2`

`-3x=6`

`x=6/(-3)`

`x=-2`

Vậy: `x=-2`

`2. x^2-4=8(x-2)`

`(x-2)(x+2)=8(x-2)`

`(x-2)(x+2)-8(x-2)`

`(x-2)(x+2-8)=0`

`(x-2)(x-6)=0`

Suy ra : `x=2` hoặc `x=6`

Vậy: `x = 2;6` 

`3. x^2-4x+4=9(x-2)`

`x^2-2*x*2+2^2=9(x-2)`

`(x-2)^2-9(x-2)=0`

`(x-2)(x-2-9)=0`

`(x-2)(x-11)=0`

Suy ra : `x=2` hoặc `x=11`

Vậy: `x = 2;11`

`4. 4x^2-12x+9=(5-x)^2`

`(2x-3)^2-(5-x)^2=0`

`(2x-3-5+x)(2x-3+5-x)=0`

`(3x-8)(x+2)=0`

`3x-8=0` hoặc `x+2=0`

Suy ra `: x=8/3` hoặc `x=-2`

Vậy  `x = 8/3 ; 2`

`5. (x-3)(x^2+3x+9)+x(x+2)(2-x)=1`

`x^3-3^3-x(x+2)(x-2)=1`

`x^3-27-x(x^2-4)=1`

`x^3-27-x^3+4x=1`

`4x-27=1`

`4x=27+1`

`4x=28`

`x=28/4 =7`

Vậy `x=7`

`6. (x+1)^3-(x-1)^3-6(x-1)^2=-10`

`x^3+3x^2+3x+1-(x^3-3x^2+3x-1)-6(x^2-2x+1)=-10`

`x^3+3x^2+3x+1-x^3+3x^2-3x+1-6(x^2-2x+1)=-10`

`6x^2-6x^2+12x-6+2=-10`

`12x-4=-10`

`12x=-10+4`

`12x=-6`

`x=-6/12 =-1/2`

Vậy ` x=-1/2`