Cubing a binomial? (x-h)(x-h)(x-h) = ?

Question

Can anyone show me how to expand (foil) this problem?

(x-h)(x-h)(x-h)

Please show work if you can! :D

Thank you so much! I promise to choose a best answer!

Answer 1

I think the easiest way is to handle 2 of the terms at a time. So, start with figuring out (x-h)(x-h) and when you have that, multipy it by the 3rd term.

To multiply 2 of your terms, you need to add up all of the parts. To get the parts, multiply each of the terms in the first binomial by each of the terms in the second binomial. i.e.
(x-h)(x-h) =
(x * x) + (x * -h) + (-h * x) + (-h * -h) =
x^2 + -xh + -xh + h^2 =
x^2 - 2xh + h^2
(the ^2 is how I can write "squared" since I can't show superscripts here - so x^2 is x squared)

Now, since this is the product of the first 2 terms, multiply it by your third term to get the answer:

(x-h)(x^2 - 2xh + h^2) =
(x * x^2) + (x * -2xh) + (x * h^2) + (-h * x^2) + (-h * -2xh) + (-h * h^2) =
x^3 - 2x^2h + xh^2 - x^2h + 2xh^2 - h^3 =
x^3 -3x^2h +3xh^2 - h^3

Answer 2

= (x^3) - 3*(x^2)*h + 3*x*(h^2) - (h^3)

Answer 3

(x-h)³