Use the Binomial Theorem to expand the binomial. (d – 4b)^3
(d - 4b)^3 = d^3 - 3d^2(4b) + 3d(4b)^2 - (4b)^3
= d^3 - 12d^2b + 48db^2 - 64b^3
show all steps
(d - 4b)^3
Using the Binomial Theorem formula for (a - b)^n, where a = d and b = 4b, and n = 3:
= C(3,0)d^3(-4b)^0 + C(3,1)d^2(-4b)^1 + C(3,2)d(-4b)^2 + C(3,3)(-4b)^3
= 1(d^3) + 3(d^2)(-4b) + 3(d)(16b^2) + 1(-64b^3)
= d^3 - 12d^2b + 48db^2 - 64b^3
Therefore, (d - 4b)^3 expands to d^3 - 12d^2b + 48db^2 - 64b^3.