Find a specific term or the general formula for a binomial expansion.
Theorem Parameters
(x + y)^5
Analysis Results
10x^3y^2
Term at k=2
The calculated term using the general formula of the binomial theorem.
Coeff10
Exponents Sum5
General Term Logic
T(2+1) = C(5, 2) · x5 - 2 · y2
About this calculator
The Binomial Theorem
The Binomial Theorem provides an algebraic method of expanding a binomial that is raised to any finite power. It states that the n-th power of a sum (x + y) can be expressed as a sum of terms involving binomial coefficients.
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Pro Tips
The (k+1)-th term uses k in the combination formula nCk.
The total number of terms is always n + 1.
The sum of the exponents of x and y in any term is always n.
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Fun Facts
"The theorem was known to Persian mathematician Al-Karaji around 1000 AD."
"It is a fundamental tool in probability theory for calculating the number of successes in n trials."
"For negative or fractional n, the expansion becomes an infinite series (Binomial Series)."
