# Finding Binomial Expansion of $(10a+b)^6$

Utilize the Binomial Expansion Calculator and enter your input term in the input field ie., $(10a+b)^6$ & press the calculate button to get the result ie., $1000000a^6 + 600000a^5b + 150000a^4b^2 + 20000a^3b^3 + 1500a^2b^4 + 60ab^5 + b^6$ 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 $(10a+b)^6$ Using Binomial Theorem

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

So $(10.a + b)^6$ = $\sum_{k=0}^6 {^6C_k}((10.a)^{6-k}(b)^{k})$

By expanding the summation:

$\frac{6!}{(6-0)!0!}(10.a)^{6-0}\times{}(b)^0+\frac{6!}{(6-1)!1!}(10.a)^{6-1}\times{}(b)^1+\frac{6!}{(6-2)!2!}(10.a)^{6-2}\times{}(b)^2+\frac{6!}{(6-3)!3!}(10.a)^{6-3}\times{}(b)^3+\frac{6!}{(6-4)!4!}(10.a)^{6-4}\times{}(b)^4+\frac{6!}{(6-5)!5!}(10.a)^{6-5}\times{}(b)^5+\frac{6!}{(6-6)!6!}(10.a)^{6-6}\times{}(b)^6$

$= \frac{720}{(720)1}(10.a)^{6-0}\times{}(b)^0+\frac{720}{(120)1}(10.a)^{6-1}\times{}(b)^1+\frac{720}{(24)2}(10.a)^{6-2}\times{}(b)^2+\frac{720}{(6)6}(10.a)^{6-3}\times{}(b)^3+\frac{720}{(2)24}(10.a)^{6-4}\times{}(b)^4+\frac{720}{(1)120}(10.a)^{6-5}\times{}(b)^5+\frac{720}{(1)720}(10.a)^{6-6}\times{}(b)^6$

$= 1(10.a)^{6-0}\times{}(b)^0+6(10.a)^{6-1}\times{}(b)^1+15(10.a)^{6-2}\times{}(b)^2+20(10.a)^{6-3}\times{}(b)^3+15(10.a)^{6-4}\times{}(b)^4+6(10.a)^{6-5}\times{}(b)^5+1(10.a)^{6-6}\times{}(b)^6$

$= (10.a)^{6-0}\times{}(b)^0+(6)(10.a)^{6-1}\times{}(b)^1+(15)(10.a)^{6-2}\times{}(b)^2+(20)(10.a)^{6-3}\times{}(b)^3+(15)(10.a)^{6-4}\times{}(b)^4+(6)(10.a)^{6-5}\times{}(b)^5+(10.a)^{6-6}\times{}(b)^6$

$= (10.a)^{6}\times{}(b)^0+(6)(10.a)^{5}\times{}(b)^1+(15)(10.a)^{4}\times{}(b)^2+(20)(10.a)^{3}\times{}(b)^3+(15)(10.a)^{2}\times{}(b)^4+(6)(10.a)^{1}\times{}(b)^5+(10.a)^{0}\times{}(b)^6$

$= (10.a)^{6}\times{}1+(6)(10.a)^{5}\times{}(b)^1+(15)(10.a)^{4}\times{}(b)^2+(20)(10.a)^{3}\times{}(b)^3+(15)(10.a)^{2}\times{}(b)^4+(6)(10.a)^{1}\times{}(b)^5+1\times{}(b)^6$

$= 1000000.a^6\times{}(1)+(6)100000.a^5\times{}(b)+(15)10000.a^4\times{}(b^2)+(20)1000.a^3\times{}(b^3)+(15)100.a^2\times{}(b^4)+(6)10.a\times{}(b^5)+1\times{}(b^6)$

$= 1000000a^6 + 600000a^5b + 150000a^4b^2 + 20000a^3b^3 + 1500a^2b^4 + 60ab^5 + b^6$

### FAQs on Binomial Expansion of $(10a+b)^6$

1. How to simplify the Binomial Expansion $(10a+b)^6$?

You can expand the given term $(10a+b)^6$ in a binomial expansion by using Newton's binomial theorem & the formula of it.

2. What is the Binomial Expansion of $(10a+b)^6$?

The Binomial Expansion of $(10a+b)^6$ is $1000000a^6 + 600000a^5b + 150000a^4b^2 + 20000a^3b^3 + 1500a^2b^4 + 60ab^5 + b^6$.

3. Where can I obtain a step by step solution to expand the given binomial $(10a+b)^6$?

You can obtain the step by step solution for Binomial Expansion of $(10a+b)^6$ on our page.