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| Math Central | Quandaries & Queries |
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Question from Laura, a student: 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 x4.
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 x4 term? What are their coefficients?
Harley
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