Question

How do you factor `27x³ - 64y³`?

Answer 1

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

Explanation:

This is a difference of 2 cubes which can be factorised as

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

for `27x^3 - 64y^3 , a = 3x color(black)(" and ") b = 4y`

substituting these into the above expression to obtain

`27x^3 - 64y^3 = (3x - 4y )( 9x^2 + 12xy + 16y^2 )`