Multiply and reduce 3x^2 (3x-6/x)

Simplify the following:

3 x^2 (3 x - 6/x)

Put each term in 3 x - 6/x over the common denominator x: 3 x - 6/x = (3 x^2) / x - 6/x:

3 x^2 (3 x^2) / x - 6/x

(3 x^2) / x - 6/x = (3 x^2 - 6) / x:

3 x^2 (3 x^2 - 6) / x

Combine powers. (3 x^2 (3 x^2 - 6)) / x = 3 x^ (2 - 1) (3 x^2 - 6):

3 x^ (2 - 1) (3 x^2 - 6)

2 - 1 = 1:

3 x (3 x^2 - 6)

Factor 3 out of 3 x^2 - 6:

3 x*3 (x^2 - 2)

3*3 = 9:

Answer: 9 x (x^2 - 2)