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

2 Answers
Apr 24, 2017

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

Apr 24, 2017

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.