3.1.5—Binomial expansion

In (a+b)^n the term containing a^{n−r}b^r is C(n,r)a^{n−r}b^r. The general term is useful for coefficients, approximations and selected powers.

Match the requested power before simplifying, include signs in b, and check whether n is a non-negative integer for a finite expansion.

The coefficient of x³ in (2−x)^5 is C(5,3)·2²·(−1)³=−40.

The row of Pascal’s triangle supplies only C(n,r); powers and signs still belong to the term.