The Binomial Expansion

Scheme of work: Year 12 A-Level: Pure 1:The Binomial Expansion

Prerequisite Knowledge

  • Be able to expand brackets.
  • Know and apply the rules of indices

Success Criteria

  • Use the Pascal triangle to identify binomial coefficients and use them to expand simple binomial expressions.
  • Find binomial coefficients using factorials and using nCr notation.
  • Use the binomial expansion to expand brackets in the form (1 + x)n, (1 + ax) n and (a + bx)n.
  • Find individual coefficients in a binomial expansion
  • Make approximations using the binomial expansion

Key Concepts

  • Introduce students to Binomial Expansion through Pascal Triangle.
  • Writing individual terms in brackets is good practice when expanding, as students can get confused with negative and fractional terms.
  • Students need to know how to use the nCr button on their calculators.
  • The binomial expansion can be used to find approximations of a number raised to a power. When approximating solutions, the value of x is so small that you can ignore the higher powers of the expansion.

Common Misconceptions

  • Students often forget that the power rule applies when raising terms such as (ax)n. For example, students incorrectly write this as ax n instead of anxn
  • Often, students forget to convert expressions in the form (a + x)n to (1 + x)n.

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