SOLUTION: what is the coefficient of the 5th term of the expansion of (2x^2 + 3y^3)^10 how about the sum of exponents of the terms in expansion

Question 1203588: what is the coefficient of the 5th term of the expansion of (2x^2 + 3y^3)^10 how about the sum of exponents of the terms in expansion

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

To find the coefficient of the th term in the expansion of , we need to use the binomial theorem.
The general term in the expansion of is given by:

where is the binomial coefficient of and , given by:

To find the th term, we need to substitute , since the first term has . Therefore, the th term is:

=
=
=

Therefore, the coefficient of the th term in the expansion of is .

Answer by greenestamps(13216) (Show Source): You can put this solution on YOUR website!

It is not clear what you are asking when, at the end of your post, you say "how about the sum of exponents of the terms in expansion"....

The first term of the expansion is , so the exponent on that term is 2*10 = 20.

The second term includes factors of and , so the exponent on that term is (2*9)+(3*1) = 21.

On the next terms the sums of the exponents will be 22, then 23, then 24...

The last term is , so the exponent on that term is 3*10 = 30.

So the sums of the exponents on successive terms of the expansion will be 20, 21, 22, ..., and 30.

RELATED QUESTIONS
How do you write the binomial expansion for question # 1 & 2? 1. (2x+3)3 < - -3rd power (answered by stanbon)
In the expansion of (x + 4y)^12, the numerical coefficient of the 5th term... (answered by MathLover1)
Consider the expansion of (x+y)^n. thanks! 1. How many terms does the expression... (answered by jim_thompson5910)
Consider the expansion of (x+y)^n. 1. How many terms does the expression contain? 2.... (answered by KMST)
what is the third term in the expansion of (2x-3y)^3 (answered by jim_thompson5910,Alan3354)
What is the coefficient of x^7 in the expansion of (2x+10)^10... (answered by Fombitz)
Find the term that has x^10 in the expansion of... (answered by robertb)
What is the coefficient of the x^6y^4 term in the expansion of... (answered by ewatrrr)
in the binomial expansion of (x+y)^8 what is the coefficient of the term containing x^3... (answered by edjones)