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

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=(8!)/(4!(8-4)!)\cdot x^4\cdot(625)=(70)(625)(x^4)=43750x^4`

Hence, the fifth terms is

`43750x^4`