Question 204279
Factor completely:
{{{3b^3-81d^3}}} First, factor out a 3.
{{{3(b^3-27d^3)}}} Now do you see that the parentheses contain the difference of two cubes?
The difference of two cubes can be factored thus:
{{{A^3-B^3 = (A-B)(A^2+AB+B^2)}}} Applying this to the group in the parentheses, we get:
{{{highlight(3(b-3d)(b^2+3bd+9d^2))}}}