# Finding Binomial Expansion of $(2+i)^4$

Utilize the Binomial Expansion Calculator and enter your input term in the input field ie., $(2+i)^4$ & press the calculate button to get the result ie., $i^4 + 8i^3 + 24i^2 + 32i + 16$ along with a detailed solution in a fraction of seconds.

Ex: (x+1)^2 (or) (x+7)^7 (or) (x+3)^4

Binomial Expansion of:

## Elaborate Steps to Expand $(2+i)^4$ Using Binomial Theorem

According to the binomial formula $(a+b)^n$ = $\sum_{k=0}^{n} {^nC_k}(a^{n-k}b^{k})$

So $(i + 2)^4$ = $\sum_{k=0}^4 {^4C_k}((2)^{4-k}(i)^{k})$

By expanding the summation:

$\frac{4!}{(4-0)!0!}(2)^{4-0}\times{}(i)^0+\frac{4!}{(4-1)!1!}(2)^{4-1}\times{}(i)^1+\frac{4!}{(4-2)!2!}(2)^{4-2}\times{}(i)^2+\frac{4!}{(4-3)!3!}(2)^{4-3}\times{}(i)^3+\frac{4!}{(4-4)!4!}(2)^{4-4}\times{}(i)^4$

$= \frac{24}{(24)1}(2)^{4-0}\times{}(i)^0+\frac{24}{(6)1}(2)^{4-1}\times{}(i)^1+\frac{24}{(2)2}(2)^{4-2}\times{}(i)^2+\frac{24}{(1)6}(2)^{4-3}\times{}(i)^3+\frac{24}{(1)24}(2)^{4-4}\times{}(i)^4$

$= 1(2)^{4-0}\times{}(i)^0+4(2)^{4-1}\times{}(i)^1+6(2)^{4-2}\times{}(i)^2+4(2)^{4-3}\times{}(i)^3+1(2)^{4-4}\times{}(i)^4$

$= (2)^{4-0}\times{}(i)^0+(4)(2)^{4-1}\times{}(i)^1+(6)(2)^{4-2}\times{}(i)^2+(4)(2)^{4-3}\times{}(i)^3+(2)^{4-4}\times{}(i)^4$

$= (2)^{4}\times{}(i)^0+(4)(2)^{3}\times{}(i)^1+(6)(2)^{2}\times{}(i)^2+(4)(2)^{1}\times{}(i)^3+(2)^{0}\times{}(i)^4$

$= (2)^{4}\times{}1+(4)(2)^{3}\times{}(i)^1+(6)(2)^{2}\times{}(i)^2+(4)(2)^{1}\times{}(i)^3+1\times{}(i)^4$

$= 16\times{}(1)+(4)8\times{}(i)+(6)4\times{}(i^2)+(4)2\times{}(i^3)+1\times{}(i^4)$

$= i^4 + 8i^3 + 24i^2 + 32i + 16$

### FAQs on Binomial Expansion of $(2+i)^4$

1. How to simplify the Binomial Expansion $(2+i)^4$?

You can expand the given term $(2+i)^4$ in a binomial expansion by using Newton's binomial theorem & the formula of it.

2. What is the Binomial Expansion of $(2+i)^4$?

The Binomial Expansion of $(2+i)^4$ is $i^4 + 8i^3 + 24i^2 + 32i + 16$.

3. Where can I obtain a step by step solution to expand the given binomial $(2+i)^4$?

You can obtain the step by step solution for Binomial Expansion of $(2+i)^4$ on our page.