How do you use the binomial series to expand g(x) = (2-x)^4?

Jan 29, 2018

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

Explanation:

As per Pascal's 4th row, cooefficients are

1 4 6 4 1

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

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