Question 330985
Factor:
{{{81c^6-3f^6}}} First factor a 3.
{{{3(27c^6-f^6)}}} Notice that the binomial is the difference of two cubes.
{{{3((3c^2)^3-(f^2)^3)}}}
The difference of two cubes can be factored thus:
{{{A^3-B^3 = (A-B)(A^2+AB+B^2)}}} and in this problem, {{{A = 3c^2}}} and {{{B = f^2}}} so making the appropriate substitutions, we get:
{{{highlight(3(3c^2-f^2)(9c^4+3c^2f^2+f^4))}}} and that's the best we can do!