# How do you use the binomial theorem to expand and simplify the expression (r+3s)^6?

Jan 29, 2018

$\textcolor{g r e e n}{{\left(r + 3 s\right)}^{6} = {r}^{6} + 18 {r}^{5} s + 135 {r}^{4} {s}^{2} + 540 {r}^{3} {s}^{3} + 1215 {r}^{2} {s}^{4} + 1458 r {s}^{5} + 729}$

#### Explanation:

As per Pascal's Triangle coefficients of the terms are

## 1 6 15 20 15 6 1

${\left(r + 3 s\right)}^{6} = {r}^{6} + 6 {r}^{5} \left(3 s\right) + 15 {r}^{4} {\left(3 s\right)}^{2} + 20 {r}^{3} {\left(3 s\right)}^{3} + 15 {r}^{2} {\left(3 s\right)}^{4} + 6 r {\left(3 s\right)}^{5} + {\left(3 s\right)}^{6}$

$\textcolor{g r e e n}{{\left(r + 3 s\right)}^{6} = {r}^{6} + 18 {r}^{5} s + 135 {r}^{4} {s}^{2} + 540 {r}^{3} {s}^{3} + 1215 {r}^{2} {s}^{4} + 1458 r {s}^{5} + 729}$