Question 1179418
.
Find the coefficient a of the given term in the expansion of the binomial.
Binomial
(x + 9)^12
Term
ax^3
~~~~~~~~~~~~~~~


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


    {{{(x+9)^12}}} = {{{sum(C[12]^k*x^(12-k)*9^k, k=0,12)}}}.


The term with x^3  is   {{{C[12]^9*x^3*9^9}}} = {{{((12*11*10)/(1*2*3))*9^9*x^3}}} = {{{85232507580*x^3}}},


so the coefficient "a" under the problem's question is  85232507580.      <U>ANSWER</U>
</pre>

Solved.


-------------


See the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Binomial-Theorem.lesson>Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/Remarkable-identities-for-Binomial-Coefficients.lesson>Remarkable identities for Binomial Coefficients</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/Permutations/The-Pascal-triangle.lesson>The Pascal's triangle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Permutations/Solved-problems-on-binomial-coefficients.lesson>Solved problems on binomial coefficients</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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



Save the link to this textbook together with its description


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.