Lesson Plan: Binomial Theorem: Negative and Fractional Exponents Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use the binomial expansion to expand binomials with negative and fractional exponents.

Objectives

Students will be able to

  • expand binomial expressions of the form (1+π‘₯), where 𝑛 is negative or a fraction,
  • expand binomial expressions of the form (π‘Ž+𝑏π‘₯), where 𝑛 is negative or a fraction and π‘Ž and 𝑏 are constants,
  • find the range of values for which a binomial expansion is valid,
  • approximate values using a binomial expansion and find the percentage error of the approximation when compared to the actual value.

Prerequisites

Students should already be familiar with

  • Pascal’s triangle,
  • factorials,
  • combinations,
  • the binomial expansion for positive integer powers.

Exclusions

Students will not cover

  • using partial fractions to find a binomial expansion.

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