Binomial Expansion

Study Guide

Terms

Terms

Terms Terms

Binomial Theorem

For any positive integer n, the expansion of (x + y)ⁿ is C(n, 0)xⁿ + C(n, 1)x^n-1y + C(n, 2)x^n-2y² + … + C(n, n - 1)xy^n-1 + C(n, n)yⁿ.
The rth term in the expansion of (x + y)ⁿ is given by C(n, r - 1)x^n-(r-1)y^r-1.
Pascal's Triangle

A triangle in which each row has one more entry than the preceding row, each row begins and ends with "1," and the interior elements are found by adding the adjacent elements in the preceding row.

Figure %: Pascal's Triangle

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