college algebra word problem

Question

Use the binomial theorem to expand the expression. Simplify the result.

(a + 4)^³

Answer 1

a^3 + 3(4)a^2 + 3(4)^2(a) + (4)^3 =

a^3 + 12a^2 + 48a + 64

a shows up in each term with descending powers, a^3, a^2, a^1, a^0

while 4 shows up in the opposite ascending order of powers, 4^0, 4^1, 4^2, 4^3

there's also coefficients of 1, 3, 3, 1,