# Finding Binomial Expansion of $(1+h)^3$

Utilize the Binomial Expansion Calculator and enter your input term in the input field ie., $(1+h)^3$ & press the calculate button to get the result ie., $h^3 + 3h^2 + 3h + 1$ 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 $(1+h)^3$ Using Binomial Theorem

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

So $(h + 1)^3$ = $\sum_{k=0}^3 {^3C_k}((1)^{3-k}(h)^{k})$

By expanding the summation:

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

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

$= 1(1)^{3-0}\times{}(h)^0+3(1)^{3-1}\times{}(h)^1+3(1)^{3-2}\times{}(h)^2+1(1)^{3-3}\times{}(h)^3$

$= (1)^{3-0}\times{}(h)^0+(3)(1)^{3-1}\times{}(h)^1+(3)(1)^{3-2}\times{}(h)^2+(1)^{3-3}\times{}(h)^3$

$= (1)^{3}\times{}(h)^0+(3)(1)^{2}\times{}(h)^1+(3)(1)^{1}\times{}(h)^2+(1)^{0}\times{}(h)^3$

$= (1)^{3}\times{}1+(3)(1)^{2}\times{}(h)^1+(3)(1)^{1}\times{}(h)^2+1\times{}(h)^3$

$= 1\times{}(1)+(3)1\times{}(h)+(3)1\times{}(h^2)+1\times{}(h^3)$

$= h^3 + 3h^2 + 3h + 1$

### FAQs on Binomial Expansion of $(1+h)^3$

1. How to simplify the Binomial Expansion $(1+h)^3$?

You can expand the given term $(1+h)^3$ in a binomial expansion by using Newton's binomial theorem & the formula of it.

2. What is the Binomial Expansion of $(1+h)^3$?

The Binomial Expansion of $(1+h)^3$ is $h^3 + 3h^2 + 3h + 1$.

3. Where can I obtain a step by step solution to expand the given binomial $(1+h)^3$?

You can obtain the step by step solution for Binomial Expansion of $(1+h)^3$ on our page.