Question

How do you multiply `(x-3)^3`?

Answer 1

See the entire solution process below:

Explanation:

We can rewrite this expression as:

`(x - 3)(x - 3)(x - 3)`

We can multiple the two terms in parenthesis on the right of the expression using this rule:

`(a - b)(a - b) = a^2 - 2ab + b^2`

Substituting `x` for `a` and `3` for `b` gives:

`(x - 3)(x - 3)(x - 3) = (x - 3)(x^2 - (2x * 3) + 9) =`

`(x - 3)(x^2 - 6x + 9)`

We now need to multiply these two terms together. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(x) - color(red)(3))(color(blue)(x^2) - color(blue)(6x) + color(blue)(9))` becomes:

`(color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(6x)) + (color(red)(x) xx color(blue)(9)) - (color(red)(3) xx color(blue)(x^2)) + (color(red)(3) xx color(blue)(6x)) - (color(red)(3) xx color(blue)(9))`

`x^3 - 6x^2 + 9x - 3x^2 + 18x - 27`

We can now group and combine like terms:

`x^3 - 6x^2 - 3x^2 + 9x + 18x - 27`

`x^3 + (-6 - 3)x^2 + (9 + 18)x - 27`

`x^3 + (-9)x^2 + 27x - 27`

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

Answer 2

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

Explanation:

`(x-3)^3` = `(x-3)(x-3)(x-3)`

Taking into account only the first two terms, we multiply to get `x^2-6x+9`.

Next, we multiply `x^2-6x+9` by `x-3`.

The result is `x^3-3x^2-6x^2+18x+9x-27`.

We simplify this by combining like terms:
`x^3-9x^2+27x-27`

And that is the answer.