Use The binomial theorem to expand the binomial.
(d-4b)^3
Using the binomial theorem, we can expand (d-4b)^3:
(d-4b)^3 = C(3,0) * (d)^3 * (-4b)^0 + C(3,1) * (d)^2 * (-4b)^1 + C(3,2) * (d)^1 * (-4b)^2 + C(3,3) * (d)^0 * (-4b)^3
Simplifying,
= 1 * d^3 * 1 + 3 * d^2 * -4b + 3 * d * 16b^2 + 1 * -64b^3
= d^3 -12d^2b + 48db^2 - 64b^3
Therefore, the expanded form of (d-4b)^3 is d^3 - 12d^2b + 48db^2 - 64b^3.