SOLUTION: Find the coefficient a of the given term in the expansion of the binomial. Binomial (x + 9)^12 Term ax^3

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Question 1179418: Find the coefficient a of the given term in the expansion of the binomial.
Binomial
(x + 9)^12
Term
ax^3
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Binomial
%28x+%2B+9%29%5E12
we need this term: ax%5E3

%2812C9%29%28x%29%5E%2812-9%29%2A9%5E9
=220x%5E3%2A387420489
=85232507580x%5E3

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the coefficient a of the given term in the expansion of the binomial.
Binomial
(x + 9)^12
Term
ax^3
~~~~~~~~~~~~~~~ 

They want you determine the term with x^3,  ax^3,  in the binomial expansion


    %28x%2B9%29%5E12 = sum%28C%5B12%5D%5Ek%2Ax%5E%2812-k%29%2A9%5Ek%2C+k=0%2C12%29.


The term with x^3  is   C%5B12%5D%5E9%2Ax%5E3%2A9%5E9 = %28%2812%2A11%2A10%29%2F%281%2A2%2A3%29%29%2A9%5E9%2Ax%5E3 = 85232507580%2Ax%5E3,


so the coefficient "a" under the problem's question is  85232507580.      ANSWER

Solved.

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See the lessons
    - Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion
    - Remarkable identities for Binomial Coefficients
    - The Pascal's triangle
    - Solved problems on binomial coefficients
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Binomial expansion, binomial coefficients, Pascal's triangle".


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Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.