# How do you use the binomial series to expand (2x – 5y)^3 ?

Jan 23, 2016

$8 {x}^{3} - 30 {x}^{2} y + 150 x {y}^{2} - 125 {y}^{3}$

#### Explanation:

The binomial theorem states that

(x+y)^n=sum_(r=0)^n""^nC_rx^(n-r)y^r.

So in this particular case we get

(2x-5y)^3=sum_(r=0)^3""^3Cr(2x)^(3-r)(-5y)^r

$= {\text{^3C_0(2x)^3+""^3C_1(2x)^2(-5y)+""^3C_2(2x)(-5y)^2+}}^{3} {C}_{3} {\left(- 5 y\right)}^{3}$

$= 8 {x}^{3} - 30 {x}^{2} y + 150 x {y}^{2} - 125 {y}^{3}$