# Thread: Find the coefficient a of the term in the expansion of this binomial

1. ## Find the coefficient a of the term in the expansion of this binomial

Find the coefficient a of the term in the expansion of this binomial

(x^2+y)^10 TERM: ax^8y^6

2. Originally Posted by thepride
Find the coefficient a of the term in the expansion of this binomial

(x^2+y)^10 TERM: ax^8y^6
The general term is $\displaystyle {10 \choose r} (x^{2})^r y^{10 - r} = {10 \choose r} x^{2r} y^{10 - r}$. What value of r will give you the required term? Use that value to get the coefficient.

3. Originally Posted by thepride
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.