The binomial theorem

Connect coefficients in polynomial expansions with combinations.

Meaning

The binomial theorem relates the coefficients in the expansion of to combination counts. It can be explained by counting which term is selected from each factor.

Example

The coefficient of is 3 because there are three choices of the factor contributing Rather than only memorizing coefficients, check that the two exponents in each term add to This finite expansion formula applies when is a nonnegative integer.

Practice for this concept

Scope and references

Topics

Binomial coefficients, Pascal's triangle, connections between expansion and combinations

Learning goal

Connect coefficients in polynomial expansions with combinations.

Helpful background

Connect polynomial expansion with counting unordered selections.

Binomial theorem

These choice exercises calculate or judge specified finite data, trials, or assumptions. They do not establish data collection, written inference, model validation, or mastery of the whole statistics area.

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