What is the product of 6(x^2-1) * 6x-1/6(x+1)

The LCD is 6.  Multiply the entire expression by 6, and then divide the result by 6:

6 [ 6(x^2-1) * 6x-1/6(x+1) ]

                6

When expanded and simplified, we get:

(36x^2 - 36)*6x - (x+1)

                 6

or:

216x^3 - 216x - x - 1

               6

Combining the two x-terms:

216x^3 - 217x -1
    (answer)
              6