Question 1181279
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Find the coefficient of x^6 in the expansion of (2x-3)^9
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<pre>
The binomial expansion is this formula


    {{{(a+b)^n}}} = {{{a^n}}} + {{{C[n]^1*a^(n-1)*b}}} + {{{C[n]^2*a^(n-2)*b^2}}} + {{{C[n]^3*a^(n-3)*b^3}}} + . . . + {{{C[n]^(n-1)*a^1*b^(n-1)}}} + {{{b^n}}}


In our case,  n = 9,  a = 2x,  b = -3.  Therefore, the general term of the binomial expansion in our case is  


    {{{C[9]^k*(2x)^(9-k)*(-3)^k}}}, k = 0, 1, 2, 3, 4, 5, . . . 


Then the term with  x^6  is the fourth term of the expansion at k = 3 


    {{{C[9]^3*(2x)^(9-3)*(-3)^3}}} = {{{((9*8*7)/(1*2*3))*2^6*x^6*(-3)^3}}} = {{{-145162*x^6}}}.    <U>ANSWER</U>
</pre>

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If you want to see other similar solved problems and to learn the subject wider and deeper, &nbsp;then look into the lesson

&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 lesson is 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.