Binomial Expansion for Positive Integer n

The binomial expansion allows us to expand expressions of the form (a + b)^n where n is a positive integer. This is a key topic in Edexcel A-Level Mathematics (9MA0) and links algebra to combinatorics.

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Key Definitions

Term	Meaning
Binomial	An expression with exactly two terms, e.g. (a + b)
Binomial expansion	The expanded form of (a + b)^n
nCr (or "n choose r")	The binomial coefficient: n! / (r!(n-r)!)
Pascal's triangle	A triangular array where each entry is the sum of the two above it
n! (n factorial)	n x (n-1) x (n-2) x ... x 2 x 1; also 0! = 1

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Pascal's Triangle

Each row gives the coefficients for expanding (a + b)^n: