Lecture 22: The Binomial Theorem

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Problem of the day

The sum of the coefficients of (x-2)^2 = 1x^2-4x+4 is 1-4+4=1. What is the sum of the coefficients in the expanded form of (2x-3y)^5?

Brief review of the lecture

The Binomial Theorem can be used to expand powers of binomials (hence the name) without recourse to polynomial multiplication or Pascal's triangle.

The rth entry in the nth row of Pascal's triangle is given by the formula

nCr = n! / [(n-r)!r!]

The number nCr is called a Binomial Coefficient. We looked a second time at several binomial expansions: (x+1)^5, (x+y)^5, (2x+1)^4, and (2-3)^4. We also looked at one more, which comes up in probability (1/3 + 2/3)^5. If you read this web page before class, you would profit from practicing these problems before the lecture.

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