Factor 9x 6 - 16y 6 completely?

This is the concept of polynomial functions, we are required to factor the polynomial of degree six given by:

9x^2-16y^6

let b=y^2

such that the expression becomes;

9x^2-16b^2

9x^2-12xb+12xb-16b^2

factoring the above we get:

3x (3x-4xb) + 4b (3x-4b)

= (3x-4b) (3x+4b)

replacing b by y^2 we get:

(3x-4y^2) (3x+4y^2)