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Binomial Theorem
High School
Definition
A formula for expanding powers of binomials using combinations as coefficients.
Formulas
(x + y)ⁿ = ∑_k=0ⁿ \binomnk x^n-k y^k
Binomial theorem
\binomn0 + \binomn1 + ·s + \binomnn = 2ⁿ
Sum of binomial coefficients
Examples
Example 1
Expand (x + 1)⁴.
History
Discovered by: Isaac Newton (17th century)
Newton generalized to negative/fractional exponents.
Applications
Probability
Binomial distribution derivation
Approximation
(1+x)ⁿ approximations
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