In the expansion of (x+y)^15, a certain term contains x^10. What is the exponent of y in this term?

a. 8
b. 9
c. 11
d. 5

Question

In the expansion of (x+y)^15, a certain term contains x^10. What is the exponent of y in this term?

a. 8
b. 9
c. 11
d. 5

asnaseer · Answer

when you expand (x+y)^15 the first term will have just x^15 and the last term will have just y^15. In between these you will get terms involving both x and y. The thing that remains the same for each term is the total of the powers of the x and y in each term will always be 15.

myininaya · Answer

So each term in the expansion will look like this
$$c x^ay^b \text{ where } a+b=15 \text{ and c is some constant} $$

anonymous · Answer

@Lulu49 are you okie from here?

anonymous · Answer

Still a bit confused. is the answer 11 or 5?

anonymous · Answer

Total of the powers is 15
You already known the power of x is 10
-> Power of y = ...

myininaya · Answer

If a=10 , then how do you solve 10+b=15
for b?

anonymous · Answer

I think the answer is 5 because it goes into both 10 and 15

anonymous · Answer

:)

myininaya · Answer

the answer is 5 because 10+5=15

anonymous · Answer

Oh alright thank you both (: