How to factor by grouping: {27x}^(3) - 75x ​

Question

How to factor by grouping:

`{27x}^(3) - 75x`
​

Answer 1

3 x (3 x - 5) (3 x + 5)

Explanation:

Factor the following:

27 x^3 - 75 x

Factor 3 x out of 27 x^3 - 75 x:

3 x (9 x^2 - 25)

9 x^2 - 25 = (3 x)^2 - 5^2:

3 x (3 x)^2 - 5^2

Factor the difference of two squares. (3 x)^2 - 5^2 = (3 x - 5) (3 x + 5):

Answer: 3 x (3 x - 5) (3 x + 5)