Binomial Expansion
The binomial theorem expands (ax + b)ⁿ into a sum of terms, each with a binomial coefficient C(n, k). This calculator computes every term, multiplies out the powers and collects the result into a polynomial in x.
Worked examples
Key terms
Frequently asked questions
What is the binomial theorem?
It states that (p + q)ⁿ equals the sum over k of C(n,k)·p^(n−k)·q^k, where C(n,k) is a binomial coefficient.
Where do the coefficients come from?
Each coefficient C(n,k) is a row of Pascal's triangle — the number of ways to choose k factors of q.
Can the exponent be negative or a fraction?
This tool handles whole-number exponents. Negative or fractional exponents give an infinite series, which is a separate topic.