Question

How do you factor `125a ^ { 3} - 27b ^ { 6}` completely?

Answer 1

`=(5a-3b^2)(25a^2 +15ab^2 +9b^2)`

Explanation:

Firstly you need to recognise that all the numbers and powers are cubes. This is called the difference of 2 cubes.

There is a set formula for this:

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

`125a^3 - 27b^6` can be regarded as being `5^3a^3 -3^3b^6`

`=(5a-3b^2)(25a^2 +15ab^2 +9b^2)`