The Binomial Expansion

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

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

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.

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