SOLUTION: find the 5th term, (5x+3)^5

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Question 1151220: find the 5th term, (5x+3)^5
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

find the 5th term,+%285x%2B3%29%5E5
use The Binomial Theorem


the 5th term is: 5C4%285x%29%5E1%2A3%5E4=5%2A5x%2A81=2025x

or, you can do it this way:
%285x%2B3%29%5E5.....expand
%285x%2B3%29%5E2%2A%285x%2B3%29%5E2%2A%285x%2B3%29
%2825x%5E2+%2B+30x+%2B+9%29%2A%2825x%5E2+%2B+30+x+%2B+9%29%2A%285x%2B3%29
%28625x%5E4+%2B+1500x%5E3+%2B+1350x%5E2+%2B+540x+%2B+81%29%2A%285x%2B3%29
3125x%5E5+%2B+9375x%5E4+%2B+11250x%5E3+%2B+6750x%5E2+%2B+2025x+%2B+243
so, the 5th term is 2025x

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


ASSUMING that the terms are written in standard from, with decreasing powers of the variable....

The 1st term is obtained from choosing the "x" term from all 5 of the factors of (5x+3).
The 2nd term is obtained from choosing the "x" term from 4 of the 5 of the factors of (5x+3) in all possible ways.
...
So the 5th term is obtained from choosing the "x" term from 1 of the 5 of the factors of (5x+3) in all possible ways. So the 5th term is

C%285%2C1%29%2A%28%285x%29%5E1%29%2A%28%283%29%5E4%29+=+%285%29%285x%29%2881%29+=+2025x