How do you use the binomial series to expand (2x+1)^4?

Jan 29, 2018

$\textcolor{b r o w n}{{\left(2 x + 1\right)}^{4} = 16 {x}^{4} + 32 {x}^{3} + 24 {x}^{2} + 8 x + 1}$

Explanation:

Refer Pascal's triangle for power 4

1 4 6 4 1

${\left(2 x + 1\right)}^{4} = {\left(2 x\right)}^{4} + 4 \cdot {\left(2 x\right)}^{3} \cdot 1 + 6 \cdot {\left(2 x\right)}^{2} \cdot {1}^{2} + 4 \cdot {\left(2 x\right)}^{1} \cdot {1}^{3} + {1}^{4}$

$\textcolor{b r o w n}{{\left(2 x + 1\right)}^{4} = 16 {x}^{4} + 32 {x}^{3} + 24 {x}^{2} + 8 x + 1}$