Finding binomial coefficients of product of two binomials Suppose the expression is given like this:
$(1+x) ^{10} (1+x)^{20}$. How can I find out the coefficient of $x^m$ in the above expression, given that $0≤m≤20$.

Using binomial expansion, the problem can be solved. For example, if m = 7, you know that 7 can be written as 7+0, 6+1, 5+2, 4+3, 3+4, 2+5, 1+6 or 0+7.
Now, using the result above, break down the expression into two separate expressions, and find the coefficient for each of the required powers of x using the formula for nth term of a binomial expansion.
