D1: Binomial Expansion

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From the DfE Mathematics AS and A-Level Content (LINK):

PLAYLIST

The Factorial Function

D1-00 [Binomial Expansion: Introducing Factorials n!]

Pascal's triangle

D1-01 [Binomial Expansion: Introducing and Linking Pascal’s Triangle and nCr]

D1-02 [Binomial Expansion: Explaining where nCr comes from]

Algebra Problems with nCr

D1-03 [nCr: Simplifying nCr Expressions]

D1-04 [nCr: Solving nCr Equations]

D1-05 [nCr: Algebraic Problem 1]

D1-06 [nCr: Algebraic Problem 2]

D1-07 [nCr: Algebraic Problem 3]

Binomial Expansion

D1-08 [Binomial Expansion: Expanding (1+x)^n]

D1-09 [Binomial Expansion: Expanding (a+b)^n]

D1-10 [Binomial Expansion: Fully Expand (1 + 3x)^4]

D1-11 [Binomial Expansion: Fully Expand (3 - 2x)^5]

D1-12 [Binomial Expansion: Fully Expand (x + 4/x)^6]

D1-13 [Binomial Expansion: Fully Expand (3x^2y - 4xy)^4

Finding a Coefficient

D1-14 [Binomial Expansion: Find the coefficient of x^6 in (2 + x)^8]

D1-15 [Binomial Expansion: Find the coefficient of x^2 in (1 + 3x)^16]

D1-16 [Binomial Expansion: Find the coefficient of x^3 in (2 - 5x)^14]

D1-17 [Binomial Expansion: Find the coefficient of x^10 in (1-2x)^5*(2+x)^7]

Approximating using Binomial Expansion

D1-18 [Binomial Expansion: Approximating 1.03^8 WITHOUT a calculator]

Further Binomial Expansion

D1-19 Binomial Expansion: EXTENSION Extending Binomial Expansion

D1-20 Binomial Expansion: Writing (a + bx)^n in the form p(1 + qx)^n

D1-21 Binomial Expansion: Find the first four terms of (1 + x)^(-1)

D1-22 Binomial Expansion: Find the first four terms of (1 + 2x)^(-2)

D1-23 Binomial Expansion: Find the first four terms of (1 - 3x)^(-3)

D1-24 Binomial Expansion: Find the first four terms of (2 + 4x)^(-5)

D1-25 Binomial Expansion: Find the first four terms of (9 - 3x)^(1/2)

The Range of Validity

D1-26 Binomial Expansion: Introducing the Range of Validity

D1-27 Binomial Expansion: Examples on Determining the Range of Validity

D1-28 Binomial Expansion: Two Trickier Binomial Expansions

D1-29 Binomial Expansion: Two Trickier Range of Validity

D1-30 Binomial Expansion: New Formula, Old Question