# Difference of Two Cubes

*There is a special case when multiplying polynomials that produces this: a^{3} - b*

^{3}## Polynomials

A polynomial looks like this:

example of a polynomial this one has 3 terms |

## Difference of Two Cubes

This is a special case when multiplying polynomials called the **Difference of Two Cubes**:

(a-b)(a^{2}+ab+b^{2}) = a^{3} - b^{3}

See why it works out so simply:

## Example from Geometry:

Take two cubes of lengths x and y:

The larger "x" cube can be split into four smaller boxes (cuboids), with box **A being a cube of size "y"**:

The volumes of these boxes are:

- A = y
^{3} - B = x
^{2}(x – y) - C = xy(x – y)
- D = y
^{2}(x – y)

But together, A, B, C and D make up the larger cube that has volume x^{3}:

x^{3} |
= | y^{3} + x^{2}(x – y) + xy(x – y) + y^{2}(x – y) |

x^{3} – y^{3} |
= | x^{2}(x – y) + xy(x – y) + y^{2}(x – y) |

x^{3} – y^{3} |
= | (x – y)(x^{2} + xy + y^{2}) |

Hey! We ended up with the same formula! Thank goodness.

## Sum of Two Cubes

There is also the "Sum of Two Cubes"

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

(a+b)(a^{2}-ab+b^{2}) = a^{3} + b^{3}