# Thread: Determine the coefficient of

1. ## Determine the coefficient of

I am looking at the problem

"Determine the coefficient of x4y6 in (2x + 3y)10"

Ok I am a little confused here.

Is this asking me to expand (2x + 3y)10 and then find the coefficent of that term in the result polynomial.

Just lost here.

Any guidance=very appreciated!

2. ## Re: Determine the coefficient of

Originally Posted by ehpoc
I am looking at the problem

"Determine the coefficient of x4y6 in (2x + 3y)10"

Ok I am a little confused here.

Is this asking me to expand (2x + 3y)10 and then find the coefficent of that term in the result polynomial.

Just lost here.

Any guidance=very appreciated!
From the binomial theorem, the general term is $\displaystyle ^nC_r (2x)^{10-r} (3y)^r = ^nC_r 2^{10-r} 3^r x^{10-r}y^r$.

Your job is to determine the value of r that gives $\displaystyle x^4 y^6$ and then use this value to evaluate the required coefficient.

3. ## Re: Determine the coefficient of

So I must look at the powers of x and y to determine r right?

so that term would look like x^n-6 y^6 so that is the 7th term right?

So the coefficient would be 10 choose 6?

4. ## Re: Determine the coefficient of

Originally Posted by ehpoc
So I must look at the powers of x and y to determine r right?

so that term would look like x^n-6 y^6 so that is the 7th term right?

So the coefficient would be 10 choose 6?
What about the contribution from the powers of 2 and powers of 3 ...??

5. ## Re: Determine the coefficient of

What about the contribution from the powers of 2 and powers of 3 ...??
I don't know....lol I forgot my notes a home could you explain what I am missing?

6. ## Re: Determine the coefficient of

Originally Posted by ehpoc
I don't know....lol I forgot my notes a home could you explain what I am missing?
I suggest you read post #2 with greater care and attention.

7. ## Re: Determine the coefficient of

Ok I get

(10C6)(2x)^4(3y)^6

=(10C6)(2^4)(3^6)x^4y^6

correct?

8. ## Re: Determine the coefficient of

Originally Posted by ehpoc
(10C6)(2x)^4(3y)^6
=(10C6)(2^4)(3^6)x^4y^6
correct?
Technically the answer is just the coefficient:
$\displaystyle \binom{10}{6}(2^4)(3^6)$