Find the coefficient a of the term in the expansion of this binomial
(x^2+y)^10 TERM: ax^8y^6
You can use Pascal's Triangle to perform Binomial Expansion. There are lots of very good explanations of how to do this on the web. Just run a search for "binomial expansion pascal triangle".
Look at the 10th row of Pascal's Triangle. To make this problem look like a 'normal' one, you can let $\displaystyle a=x^2$ and $\displaystyle b=y$. Then you'll be looking for the term when $\displaystyle a$ is to the 4th power and $\displaystyle b$ is to the 6th power.
The first number in the 10th row is the coefficient for $\displaystyle a^{10}b^{0}$. The second number is the coefficient for $\displaystyle a^9b^1$. And so on with the exponent on $\displaystyle a$ decreasing and the exponent on $\displaystyle b$ decreasing. You'll be looking for the 7th number in the 10th row.