Question

Factor Sums and Differences of cubes 27x^3 - 64y^3

Answer 1

The given question is

`27x^3-64y^3`

Simplify the expression

`3^3x^3-4^3y^3=(3x)^3-(4y)^3`

The difference of two cubes is given as

`x^3-y^3=\mleft(x-y\mright)\mleft(x^2^{}+xy+y^2\mright)`

Hence the given expression becomes

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

This gives

`(3x-4y)(9x^2+12xy+16y)`