# How do you use the binomial series to expand  (x + 3)^6?

May 14, 2017

${x}^{6} + 18 {x}^{5} + 135 {x}^{4} + 540 {x}^{3} + 1215 {x}^{2} + 1458 x + 729$

#### Explanation:

The binomial series gives you :
${\left(a + b\right)}^{6} = {a}^{6} + 6 {a}^{5} b + 15 {a}^{4} {b}^{2} + 20 {a}^{3} {b}^{3} + 15 {a}^{2} {b}^{4} + 6 a {b}^{5} + {b}^{6}$

Substitute a and b by x and 3 and you get:

${\left(x + 3\right)}^{6} = {x}^{6} + 18 {x}^{5} + 135 {x}^{4} + 540 {x}^{3} + 1215 {x}^{2} + 1458 x + 729$