Đáp án+Giải thích các bước giải:

 `(x+1)^{3}+(x+2)^{3}`

`=[(x+1)+(x+2)].[(x+1)^{2}-(x+1).(x+2)+(x+2)^{2}]`

`=(x+1+x+2).[x^{2}+2.x.1+1^{2}-(x^{2}+2x+x+2)+x^{2}+2.x.2+2^{2}]`

`=(2x+3).(2x^{2}+6x+5-x^{2}-3x-2)`

`=(2x+3).(x^{2}+3x+3)`

`=2x.(x^{2}+3x+3)+3.(x^{2}+3x+3)`

`=2x^{3}+6x^{2}+6x+3x^{2}+9x+9`

`=2x^{3}+9x^{2}+15x+9`

(*)

`(x-1)^{3}-(x+1)^{3}`

`=[(x-1)-(x+1)].[(x-1)^{2}+(x-1).(x+1)+(x+1)^{2}]`

`=(x-1-x-1).(x^{2}-2.x.1+1^{2}+x^{2}-1^{2}+x^{2}+2.x.1+1^{2})`

`=(-2).(x^{2}-2x+1+x^{2}-1+x^{2}-2x+1)`

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

`=-6x^{2}-2`

(*)

`(1-x)^{3}+(x+3)^{3}`

`=1^{3}-3.1^{2}.x+3.1.x^{2}-x^{3}+x^{3}+3.x^{2}.3+3.x.3^{2}+3^{3}`

`=1-3x+3x^{2}-x^{3}+x^{3}+9x^{2}+27x+27`

`=(x^{3}-x^{3})+(3x^{2}+9x^{2})+(27x-3x)+(1+27)`

`=12x^{2}+24x+28`

(*)

`(2x-3)^{3}-2x.(2x+1)^{2}`

`=(2x)^{3}-3.(2x)^{2}.3+3.2x.3^{2}-3^{3}-2x.[(2x)^{2}+2.2x.1+1^{2}]`

`=8x^{3}-36x^{2}+54x-27-8x^{3}-8x^{2}-2x`

`=(8x^{3}-8x^{3})-(36x^{2}+8x^{2})+(54x-2x)-27`

`=-44x^{2}+52x-27`

(*)

`(3x-1)^{3}-27x^{2}.(x+1)`

`=(3x)^{3}-3.(3x)^{2}.1+3.3x.1^{2}-1^{3}-27x^{3}-27x^{2}`

`=27x^{3}-27x^{2}+9x-1-27x^{3}-27x^{2}`

`=(27x^{3}-27x^{3})-(27x^{2}+27x^{2})+9x-1`

`=-54x^{2}+9x-1`

(*)

`(2x+1)^{3}-8x.(x-1)^{2}`

`=(2x)^{3}+3.(2x)^{2}.1+3.2x.1^{2}+1^{3}-8x.(x^{2}-2.x.1+1^{2})`

`=8x^{3}+12x^{2}+6x+1-8x^{3}+16x^{2}-8x`

`=(8x^{3}-8x^{3})+(12x^{2}+16x^{2})+(6x-8x)+1`

`=28x^{2}-2x+1`