Difference of Two Cubes

A special case when multiplying polynomials that produces a³ − b³

Polynomials

A polynomial looks like this:

example of a polynomial

Difference of Two Cubes

The Difference of Two Cubes is a special case of multiplying polynomials that looks like this:

It comes up sometimes when doing solutions, so is worth remembering.

And this is why it works out (press play):

Example from Geometry:

Let's take the "x" cube and subtract the "y" cube!

First, we split the "x" cube into four smaller boxes (cuboids), with box A being a cube of size "y":

The volumes of these boxes are:

• A = y³
• B = x²(x − y)
• C = xy(x − y)
• D = y²(x − y)

And together, A, B, C and D make up the "x" cube with volume x³:

Yes! It is the same formula as (a − b)(a² + ab + b²) = a³ − b³
Thank goodness.

Sum of Two Cubes

There's also the "Sum of Two Cubes"

By changing the sign of b in each case we get:

Note the minus in front of "ab".