Question

How do you multiply `(x+4)^3`?

Answer 1

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

Explanation:

Given: `(x + 4)^3`

`(x + 4)^3 = (x+4)(x+4)(x+4)`

Using foil and `(a + b)^2 = a^2 + 2ab + b^2`:

`(x + 4)^3 = (x^2 + 8x + 16)(x+4)`

`= x^3 + 8x^2 + 16x + 4x^2 + 32x + 64`

Add like terms:

`(x + 4)^3 = x^3 + 12x^2 + 48x + 64`

Answer 2

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

Explanation:

`"given a factor "(x+a)^3" the expansion is"`

`x^3+(a+a+a)x^2+(a^2+a^2+a^2)x+a^3`

`"here "a=4`

`(x+4)^3`

`=x^3+(4+4+4)x^2+(4^2+4^2+4^2)x+4^3`

`=x^3+12x^2+(16+16+16)x+64`

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