# How do I use the binomial theorem to expand (d-4b)^3?

Mar 15, 2018

${d}^{3} - 12 b {d}^{2} + 48 {b}^{2} d - 64 {b}^{3}$

Refer to the explanation.

#### Explanation:

${\left(d - 4 b\right)}^{3}$

Using binomial theorem,

C(3,0) * d^3*(4b)^0 - C(3,1) * d^(3-1) * (4b)^1)+C(3,2) * d^(3-2) * (4b)^2 - C(3,3)* d^(3-3) * (4b)^3
${d}^{3} - 3 \cdot {d}^{2} \cdot 4 b + 3 \cdot d \cdot 16 {b}^{2} - 64 {b}^{3}$

${d}^{3} - 12 b {d}^{2} + 48 {b}^{2} d - 64 {b}^{3}$

That's it. Hope it helps :)