Đáp án:

Giải thích các bước giải:

 `5B)`

` a)`

` ( x - 2 )^3 - x^3 - x^2 + 8 `

`= ( x^3 - 3 * x^2 * 2 + 3 * x * 2^2 - 2^3 ) - x^3 - x^2 + 8 `

`= ( x^3 - 6x^2 + 12x - 8 ) - x^3 - x^2 + 8 `

`= x^3 - 6x^2 + 12x - 8 - x^3 - x^2 + 8 `

`= ( x^3 - x^3 ) - ( 6x^2 + x^2 ) + 12x + ( 8 - 8 ) `

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

`= 0 - 7x^2 + 12x + 0 `

`= - 7x^2 + 12x`

``

`b)`

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

`= [ 1^3 - 3 * 1^2 * 2x + 3 * 1 * ( 2x )^2 - ( 2x )^3 ] - [ 1^3 + 3 * 1^2 * 2x + 3 * 1 * ( 2x )^2 + ( 2x )^3 ) ] `

`= [ 1 - 6x + 12x^2 - 8x^3 ] - [ 1 + 6x + 12x^2 + 8x^3 ] `

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

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

`= - ( 8 + 8 )x^3 + ( 12 + 12 )x - ( 6 + 6 )x + ( 1 - 1 ) `

`= - 16x^3 + 0 - 12x + 0 `

`= - 16x^3 - 12x`

``

`c)`

` x^3 + ( 2 - x )^3 + 6x^2 + 12x `

`= x^3 + ( 2^3 - 3 * 2^2 * x + 3 * 2 * x^2 - x^3 ) + 6x^2 + 12x `

`= x^3 + ( 8 - 12x + 6x^2 - x^3 ) + 6x^2 + 12x `

`= x^3 + 8 - 12x + 6x^2 - x^3 + 6x^2 + 12x `

`= ( x^3 - x^3 ) + ( 6x^2 + 6x^2 ) + ( 12x - 12x ) + 8 `

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

`= 0 + 12x^2 + 0 + 8 `

`= 12x^2 + 8 `