Bài 1:

a) $(x-2)^3$

$=x^3-3.x^2.2+3x.2^2-2^3$

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

b) $(1+x)^3$

$=1+3.1.x+3.1.x^2+x^3$

$=x^3+3x^2+3x+1$

c) $\Bigg(x-\dfrac{1}{2}\Bigg)^3$

$=x^3-3x^2.\dfrac{1}{2}+3x.\dfrac{1}{4}-\dfrac{1}{8}$

$=x^3-\dfrac{3}{2}x^2+\dfrac{3}{4}x-\dfrac{1}{8}$

d) $(2x+3)^3$

$=(2x)^3+3.(2x)^2.3+3.2x.3^2+3^3$

$=8x^3+36x^2+54x+27$

e) $(3-x)^3$

$=3^3-3.3^2.x+3.3.x^2-x^3$

$=27-27x+9x^2-x^3$

f) $\Bigg(\dfrac{1}{2}x+1\Bigg)^3$

$=\dfrac{1}{8}x^3+3.\dfrac{1}{4}x^2.1+3.\dfrac{1}{2}x.1+1$

$=\dfrac{1}{8}x^3+\dfrac{3}{4}x^2+\dfrac{3}{2}x+1$

Bài 2:

a) $x^3+3x^2+3x+1$

$=x^3+3x^2.1+3x.1+1^3$

$=(x+1)^3$

b) $x^3-12x^2+48x-64$

$=x^3-3x^2.4+3x.4^2-4^3$

$=(x-4)^3$

c) $8x^3+12x^2+6x+1$

$=(2x)^3+3.(2x)^2.1+3.2x.1+1^3$

$=(2x+1)^3$

Đáp án `+` Giải thích các bước giải `!`

Bài `1:`

`a)`

`(x-2)^3`

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

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

`b)`

`(1+x)^3`

`= 1^3+3. 1^2. x+3. 1. x^2+x^3`

`= 1+3x+3x^2+x^3`

`c)`

`(x-1/2)^3`

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

`= x^3-(3)/(2)x^2+(3)/(4)x-1/8`

`d)`

`(2x+3)^3`

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

`= 8x^3+36x^2+54x+27`

`e)`

`(3-x)^3`

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

`= 27-27x+9x^2-x^3`

`f)`

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

`= ((1)/(2)x)^3+3. ((1)/(2)x)^2. 1+3. ((1)/(2)x). 1^2+1^3`

`= (1)/(8)x^3+(3)/(4)x^2+(3)/(2)x+1`

Bài `2:`

`a)`

`x^3+3x^2+3x+1`

`= x^3+3. x^2. 1+3. x. 1+1^3`

`= (x+1)^3`

`b)`

`x^3-12x^2+48x-64`

`= x^3-3. x^2. 4+3. x. 4^2-4^3`

`= (x-4)^3`

`c)`

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

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

`= (2x+1)^3`