Binomial Expansion Coefficients
Generate coefficients of (ax+b)ⁿ from highest to lowest power.
Your numbers
Coefficients, descending powers
Use consistent units. The result follows the assumptions you enter.
Scenario comparison
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Formula
In (ax+b)^n, the coefficient of x^(n−k) is C(n,k)a^(n−k)b^k. a and b are entered constants, n is the nonnegative integer power, and k runs from zero through that power. C(n,k) is a binomial coefficient.
Generate coefficients of (ax+b)ⁿ from highest to lowest power.
Worked example
- Coefficient a
- 1
- Constant b
- 1
- Power n
- 3
- Coefficients, descending powers
- 1, 3, 3, 1
Scope and limitations
Use consistent units. The result follows the assumptions you enter.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: bb186fe99c39 · Example checked: