For example, suppose we wanted to find the coefficient for the term \(x^6y^{10}\) of the expansion \(\left(5x+2y\right)^{16}\).

You would use "n choose k" (or 16 choose 6) multiplied by the current x and y coefficients (5 and 2) to the appropriate powers.

 

This would be equivalent to: \(\frac{16!}{10!6!}5^62^{10}\) or \(128,128,000,000\).