Year 12/AS Pure Chapter 8.1 (The Binomial Expansion)

The beginning of chapter 8 is concerned with expanding binomials of the type (𝑎 + 𝑏)ⁿ, where 𝑛 is a natural number. We start by considering the well-known cases of (𝑎 + 𝑏)⁰, (𝑎 + 𝑏)¹ and (𝑎 + 𝑏)² before attempting (𝑎 + 𝑏)³ and beyond. By using the power of Pascal's triangle, we tease out the pattern underpinning binomial expansions to 𝘢𝘯𝘺 power, thus making expanding brackets to powers 4, 5 and beyond a piece of cake!

Introduction: 00:00

Solution to Warm-Up Q1: 1:10
Solution to Warm-Up Q2: 1:36
Solution to Warm-Up Q3: 4:03
Solution to Warm-Up Q4: 7:38

PASCAL'S TRIANGLE
Introduction: 8:39
Applying the triangle to coefficients of the binomial expansion: 13:16
Total Index of terms: 17:35

USING PASCAL'S TRIANGLE TO EXPAND BRACKETS
Worked Example 1a: 18:36
Worked Example 1b: 23:01
Worked Example 2: 25:31
Worked Example 3: 29:44
Worked Example 4: 36:04

Suggested Exercises: 43:01

[MrBaileyMaths]

Timestamps for smartphones and tablets:

Introduction: 00:00

Solution to Warm-Up Q1: 1:10
Solution to Warm-Up Q2: 1:36
Solution to Warm-Up Q3: 4:03
Solution to Warm-Up Q4: 7:38

PASCAL'S TRIANGLE
Introduction: 8:39
Applying the triangle to coefficients of the binomial expansion: 13:16
Total Index of terms: 17:35

USING PASCAL'S TRIANGLE TO EXPAND BRACKETS
Worked Example 1a: 18:36
Worked Example 1b: 23:01
Worked Example 2: 25:31
Worked Example 3: 29:44
Worked Example 4: 36:04

Suggested Exercises: 43:01