Find the coefficient of (x^3) in the binomial expansion of ((3x + 4)^4) in ascending powers of x.
-
A.
432 -
B.
194 -
C.
144 -
D.
108
Correct Answer: Option A
Explanation
((3x + 4)^{4} = ^{4}C_{0}(3x)^{0}(4)^{4} + ^{4}C_{1}(3x)^{1}(4)^{3} + ^{4}C_{2}(3x)^{2}(4)^{2} + ^{4}C_{3}(3x)^{3}(4)^{1} + ^{4}C_{4}(3x)^{4}(4)^{0})
(x^{3} = ^{4}C_{3}(3x)^{3}(4) = frac{4!}{3!1!} times 3^{3} times 4)
= (432x^{3})