Binomial theorem
Expands a power of a sum; the coefficients are the rows of Pascal's triangle. History: Newton, 1665 (general form).
How to work it out
- 1
The statement:
- 2
Expands a power of a sum; the coefficients are the rows of Pascal's triangle.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ (a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \]Pascal's triangle, rows 0 to 8 (computed)
| n | Coefficients | Row sum = 2āæ |
|---|---|---|
| 0 | 1 | 1 |
| 1 | 1 1 | 2 |
| 2 | 1 2 1 | 4 |
| 3 | 1 3 3 1 | 8 |
| 4 | 1 4 6 4 1 | 16 |
| 5 | 1 5 10 10 5 1 | 32 |
| 6 | 1 6 15 20 15 6 1 | 64 |
| 7 | 1 7 21 35 35 21 7 1 | 128 |
| 8 | 1 8 28 56 70 56 28 8 1 | 256 |
Questions
What is the binomial theorem?
Expands a power of a sum; the coefficients are the rows of Pascal's triangle.
Who is the Binomial theorem associated with?
Isaac Newton, Blaise Pascal.