Use The binomial theorem to expand the binomial.
(d - 4b)^3
Using the binomial theorem, we can expand the binomial (d - 4b)^3 as:
(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 this expression, we get:
(d - 4b)^3 = 1 * d^3 * 1 + 3 * d^2 * (-4b) + 3 * d^1 * (16b^2) + 1 * (64b^3)
= d^3 - 12bd^2 + 48b^2d + 64b^3
So, the expansion of (d - 4b)^3 using the binomial theorem is d^3 - 12bd^2 + 48b^2d + 64b^3.