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

2 Answers
Apr 24, 2017

Answer:

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

Answer:

#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.