SOLUTION: What is the coefficient of x^5 in the expansion of (x+3)^8?

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Question 74227: What is the coefficient of x^5 in the expansion of (x+3)^8?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The binomial expansion uses Pascal's triangle to find the coefficients. The general form of the expansion (x+y)^n is

Where is the coefficient. So we would use Pascals triangle to find the coefficients.
If you look at the 8th row of Pascal's triangle you would see
 1     8     28    56    70    56    28    8    1

So each number in this row is our which is to be multiplied by our terms.
So our expansion is And we can see that 56*3^3 is our coefficient. Or in other words since our fifth term is
our coefficient is 1512