The general term $T_{r+1}$ = C(n,r)$x^{n-r}$$y^r$ solves three main problem types:

Type 1 -- Coefficient of $x^k$: In (f(x))^n, write the general term, set the power of x equal to k, solve for r, and compute the coefficient. For products like (1+x)^m*(1-x)^n, either multiply out using convolution or simplify the product first (e.g., (1-$x^2$)^n).

Type 2 -- Term independent of x: In ($x^a$ + b/$x^c$)^n, the general term has $x^{a(n-r)-cr}$. Setting this to 0 gives r = $\frac{an}{a+c}$. If r is not a non-negative integer at most n, no independent term exists.

Type 3 -- Rational terms in irrational expansion: In ($p^{1/a}$ + $q^{1/b}$)^n, the general term has p^{$\frac{n-r}{a}$}*$q^{r/b}$. For the term to be rational, a|(n-r) and b|r simultaneously. The number of valid r values gives the count of rational terms.

For (a-b)^n, the sign alternation (-1)^r in $T_{r+1}$ is the most commonly forgotten factor. In ($ax^p$ + b/$x^q$)^n, the constants $a^{n-r}$*$b^r$ multiply C(n,r) and must not be ignored when computing the coefficient.

JEE pattern: Problems often combine two of these types, such as "find the term independent of x in (sqrt(x) + k/$x^2$)^n" which requires both the power equation and coefficient computation. Products of binomials like (1+x)^m*(1+1/x)^n are converted to a single expression before applying the general term.