Using the fact that (1 + x)^4 * (1 + x)^9 = (1 + x)^13 show (4C0 * 9C4 + 4C1*9C3 + 4C2*9C2 + 4C3*9C1 + 4C4*9C0) = 13C4

Laura,

In the binomial expansion of (1 + x)^{13}, 13C4 is the coefficient of x^{4}.

Imagine that you have expanded (1 + x)^{4} and (1 + x)^{9} and that you multiplied them together to get (1 + x)^{13}. Which terms in the expansions of (1 + x)^{4} and (1 + x)^{9} contribute to the x^{4} term? What are their coefficients?

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.