# Binomial Theorem and simplifying coefficient

• December 5th 2009, 03:38 PM
thekrown
Binomial Theorem and simplifying coefficient
6. a) Find and simplify the coefficient of a^12*b^25 in the expression (a+b)^37.

I've no clue how to separate this... it might have something to do with complex numbers as we are covering this topic but we did not do any examples like this.

• December 5th 2009, 03:52 PM
lvleph
You use the binomial theorem
$(a+b)^n = \sum_{k=0}^n {n\choose k} a^k b^{n-k}$.
• December 5th 2009, 03:57 PM
Pulock2009
the coefficient of a^12*b^25 in the expansion of (a+b)^37 is
37C25 where aCb=a!/b!(a-b)! and n!=n(n-1)(n-2).......3.2.1. we can easily simplify the coefficient. however it is a bit lengthy!.(Happy)