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Expanding Binomials Involving Substitution
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Classroom Contents
Binomial Theorem
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- 1 Prologue to Binomial Theorem (Arrangements)
- 2 Basic Binomial Expansions
- 3 Binomial Expansion: Simple Examples
- 4 Binomial Theorem & Pascal's Triangle
- 5 Binomial Theorem: Introductory Exercises
- 6 Tricky Permutations & Combinations Question
- 7 Proving Binomial Identities
- 8 Finite Series w/ Binomial Coefficients: Substitution
- 9 Finite Series w/ Binomial Coefficients: Differentiation
- 10 Finite Series w/ Binomial Coefficients: Integration (1 of 2)
- 11 Finite Series w/ Binomial Coefficients: Integration (2 of 2)
- 12 Binomial Identities: Pascal Example
- 13 Greatest Coefficient in Binomial Expansion
- 14 Evaluating Specific Binomial Coefficients
- 15 Evaluating Coefficients From Two Expansions
- 16 Proving Binomial Identities: Comparing Coefficients
- 17 Probability Question: With & Without Binomial
- 18 Pascal's Identity (1 of 2)
- 19 Pascal's Identity (2 of 2)
- 20 Expressing Terms in a Generalised Binomial Expansion
- 21 The Properties of Pascal's Triangle in nCr Notation
- 22 Introduction to nCr Notation
- 23 How are Binomial Coefficients related to Pascal's Triangle?
- 24 The Weirdness of Pascal's Triangle
- 25 An ingenious & unexpected proof of the Binomial Theorem (1 of 2: Prologue)
- 26 An ingenious & unexpected proof of the Binomial Theorem (2 of 2: Proof)
- 27 Demonstrating the Binomial Theorem from Pascal's Triangle
- 28 Sierpinski's Triangle
- 29 Factorials
- 30 Determining & Calculating the Greatest Term (example question)
- 31 Finding & Evaluating the Greatest Coefficient (example question)
- 32 Relating Consecutive Coefficients (and finding the greatest one)
- 33 What is the Greatest Coefficient (and why do we care about it)?
- 34 Binomial Identity with Even Coefficients Only?
- 35 Binomial / Permutations & Combinations Proof (1 of 2)
- 36 Binomial / Permutations & Combinations Proof (2 of 2)
- 37 Recognising & Substituting Part of a Binomial Expansion
- 38 Simplifying Products w/ Factorial Notation
- 39 What power of 2 is a factor of "100!"?
- 40 Identifying the Constant Term in a Binomial Expansion
- 41 Expanding Binomials Involving Substitution
- 42 Separating Rational & Irrational Components in Binomial Expansion
- 43 Stating the Binomial Theorem w/ Factorial Notation
- 44 Developing the Binomial Theorem w/ Pascal's Triangle
- 45 Introduction to Factorial Notation (1 of 2: Why use "!"?)
- 46 Introduction to Factorial Notation (2 of 2: How to simplify factorial terms)
- 47 Shorthand Notation for nCr
- 48 Approximating a Decimal Expansion with Binomial Theorem
- 49 Why do all rows of Pascal's triangle add to powers of 2?
- 50 Sigma Notation & Properties of Pascal's Triangle
- 51 nCr Notation
- 52 Why Notation & Terminology Are Awesome, Not Boring
- 53 Binomial Expansions - Simple Example
- 54 Binomial Coefficients & Pascal's Triangle
- 55 Evaluating Specific Binomial Coefficients (Exam Questions)
- 56 Summing Binomial Coefficients (Exam Question)
- 57 Binomial Coefficients Proof Question
