Unit 2 – binomial theorem

The lessons and sequences in this program of learning are designed to allow students to explore using the binomial theorem to expand binomial expressions by selecting and applying appropriate algebraic techniques and prove identities involving binomial coefficients by substituting into algebraic expressions, comparing coefficients or applying a combinatorial argument.

Introduction

The binomial theorem (DOCX 7.5 MB)

Lesson 1 – Pascal's triangle

• Pascal’s triangle (DOCX 6.3 MB)
• Pascal’s triangle – slide deck (PPTX 1.5 MB)

Lesson 2 – combinatorial patterns

• Combinatorial patterns (DOCX 6.6 MB)
• Combinatorial patterns – slide deck (PPTX 1.5 MB)

Lesson 3 – the binomial theorem

• The binomial theorem (DOCX 7.5 MB)
• The binomial theorem – slide deck (PPTX 1.6 MB)

Lesson 4 – finding coefficients and the constant term

• Finding coefficients and the constant term (DOCX 8.2 MB)
• Finding coefficients and the constant term – slide deck (PPTX 1.7 MB)

Lesson 5 – comparing coefficients

• Comparing coefficients (DOCX 7.3 MB)
• Comparing coefficients – slide deck (PPTX 8.5 MB)

Lesson 6 – further proofs

• Further proofs (DOCX 6.3 MB)
• Further proofs – slide deck (PPTX 8.8 MB)