Write the indicated term of the binomial expansion.
-$( 2 x + 5 ) ^ { 5 }$; 5th term
A) $1250 x$
B) 15,625
C) $2500 x ^ { 2 }$
D) $6250 \mathrm { x }$

Question

Quizplus · Accepted Answer

The 5th term of the binomial expansion $(2x + 5)^5$ can be found using the formula for the $k$th term of a binomial expansion, which is $\binom{n}{k-1}a^{n-(k-1)}b^{k-1}$, where $n$ is the power of the binomial, $a$ and $b$ are the terms of the binomial, and $k$ is the term number. For the 5th term, $k = 5$, $n = 5$, $a = 2x$, and $b = 5$. Thus, the 5th term is $\binom{5}{4}(2x)^{5-4}(5)^4 = 5 \cdot 2x \cdot 625 = 6250x$.

Write the Indicated Term of the Binomial Expansion (2x+5)5( 2 x + 5 ) ^ { 5 }(2x+5)5

Write the Indicated Term of the Binomial Expansion $( 2 x + 5 ) ^ { 5 }$