1974 AHSME Problems/Problem 3
Contents
[hide]Problem
The coefficient of in the polynomial expansion of
is
Solution 1
Let's write out the multiplication, so that it becomes easier to see.
We can now see that the only way to get an is by taking three and one . There are way to pick which term the comes from, and the coefficient of each one is . Therefore, the coefficient of is .
Solution 2
Note that . By the binomial theorem, the term is . Therefore the coefficient is .
See Also
1974 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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