Binomial Theorem Expansion Calculator
Binomial Expansion Calculator (ax+b)^n
Enter the coefficients a, b and the power n. The tool writes every term T_{k+1} with its binomial coefficient Cₙᵏ. Turn on the advanced option to find the coefficient of x^k.
The calculator above expands (ax + b)ⁿ term by term with the binomial theorem and finds the coefficient of any power of x.
Formulas used
(a + b)ⁿ = Σ Cₙᵏ aⁿ⁻ᵏ bᵏ
General term: Tₖ₊₁ = Cₙᵏ aⁿ⁻ᵏ bᵏ
- The expansion has n + 1 terms.
- The coefficients follow Pascal’s triangle.
Worked example
Expand (x + 2)³:
(x + 2)³ = x³ + 6x² + 12x + 8
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Enter a, b, the exponent n, and optionally the power k.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.