Trap 1: Confusing the term number with the coefficient index. $T_{r+1}$ has binomial coefficient C(n,r), not C(n,r+1).

Trap 2: Forgetting that in (a - b)^n, the general term has (-1)^r. $T_{r+1}$ = C(n,r)$a^{n-r}$(-b)^r = (-1)^r * C(n,r) * $a^{n-r}$ * $b^r$.

Trap 3: In "coefficient of $x^k$" problems, students forget to account for all factors. In (2x + 3/x)^8, the coefficient of $x^2$ includes the factor 2^{n-r} * 3^r as well as C(n,r).

Trap 4: When finding the sum of coefficients, put x = 1 in the entire expression (not just in the binomial coefficient). Sum of coefficients of (2x - 1)^n is (2-1)^n = 1, not 2^n.

Trap 5: For generalized binomial series, forgetting the convergence condition |x| < 1. The series (1+x)^{-1} = 1 - x + $x^2$ - ... is valid only for |x| < 1.