Question

How do you factor the sum or difference of two cubes `64m^3n^3+216m^3p^3`?

Answer 1

8`m^3` (2n+3p) (4`n^2` -6np + 9`p^2`)

Write the numbers as perfect cubes by first taking out 8`m^3` as a common factor like this 8`m^3`{ `(2n)^3` + `(3p)^3`}. Using the algebraic identity for factorising the sum of two cubes, the factorisation would be 8`m^3` (2n+3p) (4`n^2` -6np + 9`p^2`)