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

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