Question

What is difference of two cubes method for factoring?

Answer 1

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`