Question

How do you factor 64x^3 - 27y^3?

Answer 1

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

Explanation:

First, we know that the way to factor difference of cubes is:
`color(red)(a)^3-color(blue)(b)^3 = (color(red)(a)-color(blue)(b))(color(red)(a)^2 + color(red)(a)color(blue)(b) + color(blue)(b)^2)`

Following this, we first know that:
`color(red)(root(3)(64x^3) = 4x)`

and

`color(blue)(root(3)(27y^3) = 3y)`

Based on this, we know that:
`color(red)(a)^2 = (color(red)(4x))^2 = 16x^2`

and

`color(blue)(b)^2 = (color(blue)(3y))^2 = 9y^2`

Lastly, we know that:
`color(red)acolor(blue)b = (color(red)(4x))(color(blue)(3y)) = 12xy`

Combining all this together, we know that the factored form is:
`(4x-3y)(16x^2 + 12xy + 9y^2)`

Hope this helps!