What is difference of two cubes method for factoring?

1 Answer
Apr 18, 2015

The difference of two cubes can be factored by the formula:

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

You can verify that the formula is correct by multiplying the right side of the equation. Multiplying a times each term in the secon factor and the -b times each, we get:

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

As you can see, this simplifies to: a^3-b^3