Integer Binomial Expansion
Integer Binomial Expansion with explicit inputs, formulas and domain checks.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Exact BigInt coefficients; degree0–50. Every power, including missing terms with zero coefficient, is represented.
Example Calculation
- Integer a in (ax+b)^n: 1
- Integer b: 2
- Exponent n: 3
(x+2)³=x³+6x²+12x+8.
Frequently asked questions
How do I use this calculator?
Enter integer a in (ax+b)^n, integer b, exponent n. The result updates automatically. Use Reset to restore the example values.
What method does it use?
Coefficient of x^(n−k) is C(n,k)a^(n−k)b^k.. Exact BigInt coefficients; degree0–50. Every power, including missing terms with zero coefficient, is represented.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.