Binomial Expansion Calculator
Expand binomials using the binomial theorem. Enter (a + b)^n to get the expanded form and binomial coefficients.
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isCalculator Editorial Team
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How to use this tool?
How to Use the Binomial Expansion Calculator
This tool expands expressions of the form (a + b)n using the binomial theorem. Follow these steps:
- Enter the first term (a) – Type the variable or number for a (e.g.,
x,2y). - Enter the second term (b) – Type the value for b (e.g.,
2,-3z). - Set the exponent (n) – Input a non-negative integer (e.g.,
3,5). - Click "Expand" – The calculator will display the expanded form and the formula steps.
Important notes:
- Both a and b must be non-empty.
- The exponent n must be a whole number (0, 1, 2, ...).
- Results show each term with coefficients and powers, e.g.,
x^3 + 6x^2 + 12x + 8.
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Frequently Asked Questions
The binomial theorem describes the algebraic expansion of powers of a binomial, i.e., (a + b)^n = Σ_{k=0}^{n} C(n,k) a^(n-k) b^k.
A binomial coefficient C(n,k) is the number of ways to choose k items from n, calculated as n!/(k!(n-k)!).
Yes, you can enter any algebraic expressions for a and b, such as x, 2y, or -3.
