Illinois State University Mathematics Department

MAT 305: Combinatorics Topics for K-8 Teachers

Review: Binomial & Multinomial Expansions

Here are several problems to help review our discussion of the binomial and multinomial expansions. Click on the highlighted word to take you to a possible solution or hint for that problem.
  1. Expand (r + s)^3.
  2. Write the first three terms, beginning with the term containing the factor m^7, in the expansion of (4m - 3t)^7.
  3. After expanding and collecting all like terms, how many terms will there be in the expansion of (w + v)^18 ?
  4. Is r^4st^2v^3 a possible term in the expansion of (r + s + t +v)^12 ? Explain.
  5. Determine the coefficient for the collected term containing the factor a^2b^4cd in the expansion of (a + b + c + d)^8.
  6. Create a counting problem for which 9!/(2!4!3!) is the numerical solution.

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Possible Solutions to Review Problems

1. r^3+3r^2s+3rs^2+s^3
2. 4^7m^7-3(4^6)m^6t+9(4^5)m^5t^2
3. 19
4. No. Its exponents do not sum to 12.
5. [8!/(2!4!1!1!)](a^2b^4cd)
6. Example: How many different arrangements are there for the letters in the nonsense word aabbbbccc?

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