Question

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

Answer 1

`x^5-15x^4+90x^3-270x^2+ 405x-243`.

Explanation:

`(a+b)^n=a^n+nC1 a^(n-1) b+nC2 a^(n-2) b^2 +.. nCn-r a^(n-r) b^r +... + nCn b^n`
Here, a = x, b = `-3` and n = 5.
nCr = `(n!)/(r!(n-r)!)`
nCr = nCn-r.
nCo = nCn = 1