Binomial Expansion
Algebra
Full expansion of (a + b)ⁿ with each term and coefficient.
Inputs
Expanding (a + b)^n via the binomial theorem.
Summary
Term-by-term table
| k | C(n, k) | a^(n−k) | b^k | Term value |
|---|---|---|---|---|
| 0 | 1 | 1 | 1 | 1 |
| 1 | 5 | 1 | 1 | 5 |
| 2 | 10 | 1 | 1 | 10 |
| 3 | 10 | 1 | 1 | 10 |
| 4 | 5 | 1 | 1 | 5 |
| 5 | 1 | 1 | 1 | 1 |
Pascal's triangle (row 5 highlighted)
Frequently asked questions
▶What does the Binomial Expansion do?
The Binomial Expansion is an interactive algebra lab where you change inputs and the answers update live, helping you build intuition without doing the arithmetic by hand.
▶Who should use the Binomial Expansion?
Students from primary to senior secondary classes, parents helping with homework, and anyone revising algebra can use this lab to check answers and explore "what-if" scenarios.
▶Is the Binomial Expansion free to use?
Yes. Every lab on math.suparnpatra.com is free and runs entirely in your browser : nothing is sent to a server.
▶Does the Binomial Expansion work offline?
Once the page is loaded, all calculations run locally in JavaScript, so you can keep using it even on a flaky connection.
▶How accurate are the results?
Results use standard JavaScript double-precision arithmetic and the textbook formula for algebra. We never display scientific notation : numbers are shown as ordinary decimals you can read at a glance.