Binomial Theorem

The prefix bi — as in bicycle, binocular, binary — means two. A binomial expression is simply an expression with two terms: $(1+x)$, $(x+y)$, $(x^2+xy)$, $(2a+3b)$ are all binomials.

Recall from Chapter 4 the combination symbol

$^nC_r = \frac{n(n-1)(n-2)\cdots(n-(r-1))}{r(r-1)(r-2)\cdots1} = \frac{n!}{(n-r)!\,r!}.$ …