Question

What is the fifth term in the binomial expansion of (x + 5)^8?O 175,000x³O 43,750x4O 3,125x5O 7,000x

Answer 1

Solution:

Given the expression below

$(x+5)^8$

Applying the binomial theorem formula

$\begin{gathered} \left(a+b\right)^n=\sum_{k=0}^n{\binom{n}{k}}a^{n-k}b^k \\ Where \\ a=x \\ b=5 \\ n=8 \\ k=4\text{ i.e. fifth term} \end{gathered}$

For the fifth term, i.e

$\sum_{k=4}^8{\binom{8}{4}}x^{8-4}5^4=\frac{8!}{4!(8-4)!}\cdot x^4\cdot(625)=(70)(625)(x^4)=43750x^4$

Hence, the fifth terms is

$43750x^4$