# 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.

## The Binomial Expansion Resources

### Mr Mathematics Blog

#### Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods

#### T- Formulae

Scheme of work: A-Level Further Mathematics: Further Pure 1: The t – formulae

#### Regression, Correlation and Hypothesis Testing

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Statistics: Regression, Correlation and Hypothesis Testing