Write the indicated term of the binomial expansion.
-$( 2 x + 8 ) ^ { 3 } ; \quad 3$ rd term
A) 64
B) $768 x$
C) $384 x$
D) $96 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The third term of the binomial expansion $(a + b)^n$ can be found using the formula for the $k$th term: $T_k = \binom{n}{k-1} a^{n-k+1} b^{k-1}$. For the third term ($k=3$) of $(2x + 8)^3$, we have $n=3$, $a=2x$, and $b=8$. Thus, $T_3 = \binom{3}{2} (2x)^{2} (8)^{1} = 3 \cdot 4x^2 \cdot 8 = 96x^2 \cdot 8 = 384x^2$.

Write the Indicated Term of the Binomial Expansion (2x+8)3;3( 2 x + 8 ) ^ { 3 } ; \quad 3(2x+8)3;3

Write the Indicated Term of the Binomial Expansion $( 2 x + 8 ) ^ { 3 } ; \quad 3$