SOLUTION: Find the 6th term of (-4a+3b)^13

  1-st term               2-nd term              3-rd term             4-th term             5-th term            6-th term

               


The 6-th term is   (the general formula is  ,  k = 0 (first term), 1 (the 2-nd term), 2 (the 3-rd term), . . . ).

Or, after simplifying,  =  =  = .


 =  =  = 1287  is the number of combination 13 things taken 5 at a time.


On combinations, see the lesson Introduction to Combinations in this site.


On binomial expansion see the lesson Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion.

Use the formula for a specific term in a binomial expansion: 

, where r = term number



6th term of 

6th term of 

6th term of  =