Determining coefficient of binomial expression

[eric12872]

Determine the coefficient of x^3y^10 in the binomial expression of (x+y)^13

Can someone break this one down for me so I can learn how to do it?

 

[Quaid]

Hello Eric:

Are you familiar with Pascal's Triangle? That shows the coefficients.

Check out some lessons, by googling keywords determining coefficients binomial expression. The process is basic and mechanical.

Let us know, if you still have questions.

Cheers

 

[Deleted member 4993]

Determine the coefficient of x^3y^10 in the binomial expression of (x+y)^13

Can someone break this one down for me so I can learn how to do it?

Eric,

Did you find the answer to your question?

 

[HallsofIvy]

The coefficient of \(\displaystyle x^iy^{n-i}\) in \(\displaystyle (x+ y)^n\) is the "binomial coefficient"
\(\displaystyle \begin{pmatrix}n \\ i \end{pmatrix}= \frac{n!}{i!(n- i)!}\)