What this calculator does
Binomial expansion works out expands (x + y)ⁿ term by term using the binomial theorem. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
Formula(x+y)ⁿ = Σₖ C(n,k) xⁿ⁻ᵏ yᵏ for k = 0 to n
The inputs explained
| Field | What to enter |
|---|---|
| Power (n) | A number. Starts at 5. |
| Value of x | A number. Starts at 2. |
| Value of y | A number. Starts at 3. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with power (n)
Every other input is held at the calculator’s starting values while power (n) varies. Select any row to load that scenario into the calculator.
How the answer changes with power (n)
| Power (n) | Coefficients (row of Pascal triangle) | Number of terms | Sum of all coefficients (2ⁿ) |
|---|---|---|---|
| 2.5 | 1, 3, 3, 1 | 4 | 8 |
| 3.75 | 1, 4, 6, 4, 1 | 5 | 16 |
| 5 | 1, 5, 10, 10, 5, 1 | 6 | 32 |
| 7.5 | 1, 8, 28, 56, 70, 56, 28, 8, 1 | 9 | 256 |
| 10 | 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1 | 11 | 1,024 |
| 15 | 1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1 | 16 | 32,768 |