Question 1033553
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Find the seventh term of (x+3)^9
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It is {{{C[9]^6*x^3*3^6}}} = {{{84*x^3*3^6}}} = {{{61236*x^3}}},

where {{{C[9]^6}}} = {{{(9*8*7*6*5*4)/(1*2*3*4*5*6)}}} = {{{3*4*7}}} = 84

is the corresponding coefficient of the binomial expansion, equal to the number of combinations of 9 things taken 6 at a time.

On the binomial expansion read this lesson  <A HREF=https://www.algebra.com/algebra/homework/Permutations/Binomial-Theorem.lesson>Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion</A>.

On the combinations read this lesson  <A HREF=https://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>. 

One more useful link is this lesson  <A HREF=https://www.algebra.com/algebra/homework/Permutations/The-Pascal-triangle.lesson>The Pascal's triangle</A> in this site.

<U>Answer</U>. The seventh term of  {{{(x+3)^9}}}  is  {{{61236*x^3}}}.
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