# StudySquare

# Binomial expansion

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A factorial is the product of all whole numbers smaller than or equal to a given number. The symbol of the factorial function is !. Factorials can be calculated on a calculator by pressing the number followed by the factorial button (!).

Pascal's triangle is a triangular pattern of numbers, beginning with a 1 on top, that are arranged so that each number is the sum of the two numbers directly above it. It can be used to determine the coefficients of a binomial expansion. When expanding a binomial of the type (x+y)n, the coefficients correspond to the numbers in the nth row of Pascal?s triangle (counting the top row, consisting of a 1, as the 0th row).

For brackets with larger powers, it can be impractical to use Pascal's Triangle to determine the coefficients. Instead, they can be calculated by the formula NC(r) (see image). There is a button on the calculator for this. If n is a positive integer, the bracket can then be expanded using the binomial theorem: (a + b)n = an + (nC1)anโ1b + (nC2)anโ2b2 + โฆ + (nCnโ1)abnโ1 + bn.

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# โ

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