# How do you expand (2b-x)^4?

Jan 7, 2017

$16 {b}^{4} - 32 {b}^{3} x + 24 {b}^{2} {x}^{2} - 8 b {x}^{3} + {x}^{4}$

#### Explanation:

Using Pascal's triangle for the coefficients of ${\left(x + a\right)}^{4}$ to be 1,4,6,4,1, the expansion of ${\left(2 b - x\right)}^{4}$ would be

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

On simplification it becomes

$16 {b}^{4} - 32 {b}^{3} x + 24 {b}^{2} {x}^{2} - 8 b {x}^{3} + {x}^{4}$