Question

How do you factor #27 - 125x^3?

Answer 1

`(3 - 5x)(9 +15x +25x^2)`

Explanation:

This is a `color(blue) " difference of 2 cubes "`

`27- 125x^3 = 3^3 - (5x)^3`

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

For this question let a = 3 and b = 5x

`rArr 27-125x^3 = (3-5x)(3^2+ (3xx5x) + (5x)^2 )`

`= (3 - 5x )(9 + 15x + 25x^2)`