You can put this solution on YOUR website! factor out df to get:
16d^3f - 64d^2f + 48df = df * (16d^2 - 64d + 48)
factor out 16 to get:
16df * (d^2 - 4d + 3)
factor d^2 - 4d + 3 to get:
16df * (d-3) * d-1)
i believe that will be your answer.
to confirm the factoring is correct, choose a random value of d and a random value of f and evaluate the original equation and the simplified equation.
when i chose d = 5 and f = 3.
the original equation becomes:
16 * 5^3 * 3 - 64 * 5^2 * 3 + 48 * 5 * 3 = 1920
the simplified equation becomes:
16 * 5 * 3 * 2 * 4 = 1920
you get the same answer, indicating that the factorization was done correctly.
