Find the coefficient of the given term when (u^2 - v^2 ) ^10 expanded by the binomial theorem?

Question

The term is u^16 v^4

When (u^2 - v^2 ) ^10 is exanded by the binomial theorem.

My book uses Combinations, but I'm not sure if it works if u and v are squared?

Answer 1

Put $x=u^2$, $y=v^2$, and you are reduced to looking for the $x^8 v^2$ term in $(x+y)^{10}$. So it makes essentially no difference that there are squares: you'll still get $\binom{10}{8}$ as the answer.