Binomial Theorem
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Tap a term to see what it means, or .
Calculate
Example: expand (a + b)⁵ with a = 0.7 and b = 0.3. Since a + b = 1, each term is a binomial probability, and they add up to 1. Change the values to work out your own case.
Step by step
What each term means
- The Power ((a + b)ⁿ)
- The product of n brackets (a + b). Multiplying everything out, each term picks a or b from each bracket.
- Sum from k = 0 to n
- One term for each number k of b's picked: n + 1 terms in all.
- Binomial Coefficient (C(n, k))
- How many ways to pick the k brackets that give b. These are the numbers in row n of Pascal's triangle.
- Power of a (aⁿ⁻ᵏ)
- The remaining n − k brackets give a.
- Power of b (bᵏ)
- The k brackets picked give b. The exponents of a and b always add up to n.