Question

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

Answer 1

`8x^3-30x^2y+150xy^2-125y^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`

`=""^3C_0(2x)^3+""^3C_1(2x)^2(-5y)+""^3C_2(2x)(-5y)^2+""^3C_3(-5y)^3`

`=8x^3-30x^2y+150xy^2-125y^3`