# How do you expand (2a+b)^6?

Jan 28, 2018

$\textcolor{b l u e}{64 {a}^{6} + 192 {a}^{5} b + 240 {a}^{4} {b}^{2} + 160 {a}^{3} {b}^{3} + 60 {a}^{2} {b}^{4} + 12 a {b}^{5} + {b}^{6}}$

#### Explanation:

1 6 15 20 15 6 1

Using Pascal's triangle,
(x+y)^6 where
x = 2a & y = b

${\left(2 a + b\right)}^{6} = 1 \cdot {\left(2 a\right)}^{6} + 6 {\left(2 a\right)}^{5} b + 15 {\left(2 a\right)}^{4} {b}^{2} + 20 {\left(2 a\right)}^{3} {b}^{3} + 15 {\left(2 a\right)}^{2} {b}^{4} + 6 \left(2 a\right) {b}^{5} + 1 \cdot {b}^{6}$

$64 {a}^{6} + 192 {a}^{5} b + 240 {a}^{4} {b}^{2} + 160 {a}^{3} {b}^{3} + 60 {a}^{2} {b}^{4} + 12 a {b}^{5} + {b}^{6}$