Question

How to factor `16x^9` + `54y^3` using difference of cubes?

Answer 1

`16x^9+54y^3=2(2x^3+3y)(4x^4-6x^3y+9y^2)`

Explanation:

Here we have sum of cubes and not difference of cubes. Hence, we have to use `a^3+b^3=(a+b)(a^2-ab+b^2)`. As such

`16x^9+54y^3`

= `2(8x^9+27y^3)`

= `2((2x^3)^3+(3y)^3)`

= `2((2x^3)+(3y))((2x^3)^2-(2x^3)(3y)+(3y)^2)`

= `2(2x^3+3y)(4x^4-6x^3y+9y^2)`