# Finding Binomial Expansion of $(10+7x)^2$

Utilize the Binomial Expansion Calculator and enter your input term in the input field ie., $(10+7x)^2$ & press the calculate button to get the result ie., $49x^2 + 140x + 100$ 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 $(10+7x)^2$ Using Binomial Theorem

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

So $(7.x + 10)^2$ = $\sum_{k=0}^2 {^2C_k}((10)^{2-k}(7.x)^{k})$

By expanding the summation:

$\frac{2!}{(2-0)!0!}(10)^{2-0}\times{}(7.x)^0+\frac{2!}{(2-1)!1!}(10)^{2-1}\times{}(7.x)^1+\frac{2!}{(2-2)!2!}(10)^{2-2}\times{}(7.x)^2$

$= \frac{2}{(2)1}(10)^{2-0}\times{}(7.x)^0+\frac{2}{(1)1}(10)^{2-1}\times{}(7.x)^1+\frac{2}{(1)2}(10)^{2-2}\times{}(7.x)^2$

$= 1(10)^{2-0}\times{}(7.x)^0+2(10)^{2-1}\times{}(7.x)^1+1(10)^{2-2}\times{}(7.x)^2$

$= (10)^{2-0}\times{}(7.x)^0+(2)(10)^{2-1}\times{}(7.x)^1+(10)^{2-2}\times{}(7.x)^2$

$= (10)^{2}\times{}(7.x)^0+(2)(10)^{1}\times{}(7.x)^1+(10)^{0}\times{}(7.x)^2$

$= (10)^{2}\times{}1+(2)(10)^{1}\times{}(7.x)^1+1\times{}(7.x)^2$

$= 100\times{}(1)+(2)10\times{}(7.x)+1\times{}(49.x^2)$

$= 49x^2 + 140x + 100$

### FAQs on Binomial Expansion of $(10+7x)^2$

1. How to simplify the Binomial Expansion $(10+7x)^2$?

You can expand the given term $(10+7x)^2$ in a binomial expansion by using Newton's binomial theorem & the formula of it.

2. What is the Binomial Expansion of $(10+7x)^2$?

The Binomial Expansion of $(10+7x)^2$ is $49x^2 + 140x + 100$.

3. Where can I obtain a step by step solution to expand the given binomial $(10+7x)^2$?

You can obtain the step by step solution for Binomial Expansion of $(10+7x)^2$ on our page.