Question

How do you factor `54x^3-16y^3`?

Answer 1

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

Explanation:

There is a common factor of 2 , thus

`= 2(27x^3 - 8y^3)`

Now `27x^3 - 8y^3 " is a difference of cubes "`

which factors as follows:

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

For `27x^3 , a = 3x " and for " 8y^3 , b = 2y`

`rArr 27x^3 - 8y^3 = (3x-2y)(9x^2+6xy+4y^2)`

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