How does the Binomial Theorem Calculator work?

(a + b)ⁿ = Σ C(n,k) × aⁿ⁻ᵏ × bᵏ Then: Coefficients C(n,k) = n! / (k!(n−k)!) Then: Coefficients form Pascal's triangle Then: (a+b)² = a² + 2ab + b².

Can you give an example of how to use the Binomial Theorem Calculator?

Example: Input (a+b)³ gives a result of a³ + 3a²b + 3ab² + b³.

Is the Binomial Theorem Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Binomial Theorem Calculator?

Our Binomial Theorem Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Matematică

Binomial Theorem Calculator

Binomial Expansion (a + b)ⁿ

n (power, max 15)

The binomial theorem describes how to expand expressions of the form (a + b)ⁿ. It uses Pascal's triangle coefficients and is fundamental to algebra, probability, and combinatorics.

Symbol	Name	Unit	Description
n	exponent	—	non-negative integer
a, b	terms being expanded	—	—
C(n,k)	binomial coefficient	—	"n choose k"

n	Coefficients
0	1
1	1 1
2	1 2 1
3	1 3 3 1
4	1 4 6 4 1
5	1 5 10 10 5 1

References

›Binomial theorem — Khan Academy

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Binomial Theorem Calculator

Binomial Expansion (a + b)ⁿ

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Pascal's Triangle (Coefficients)

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Binomial Expansion (a + b)ⁿ