How do you use the binomial (3-2z)^4 using Pascal's triangle?

Jan 29, 2018

$\textcolor{g r e e n}{{\left(3 - 2 z\right)}^{4} = 243 - 216 z + 216 {z}^{2} - 96 {z}^{3} + 16 {z}^{4}}$

Explanation:

As seen from the Pascal's triangle,

1 4 6 4 1

${\left(3 - 2 z\right)}^{4} = 1 \cdot {3}^{4} \cdot {\left(2 z\right)}^{0} - 4 \cdot {3}^{3} \left(2 z\right) + 6 \cdot {3}^{2} {\left(2 z\right)}^{2} - 4 \cdot 3 \cdot {\left(2 z\right)}^{3} + 1 \cdot {3}^{0} \cdot {\left(2 z\right)}^{4}$

$\textcolor{g r e e n}{{\left(3 - 2 z\right)}^{4} = 243 - 216 z + 216 {z}^{2} - 96 {z}^{3} + 16 {z}^{4}}$