Multiply Binomials Calculator: Expand Products Step by Step
This multiply binomials calculator expands the product of two binomials and shows every step. Enter (2x + 3)(x − 1), and it returns 2x² + x − 3.
Use the Multiply Binomials Calculator
Type two binomials in parentheses and select Calculate. You'll see the four products (First, Outer, Inner, Last), the combined like terms, and the simplified polynomial in standard form.
Input tips
- Write each binomial in parentheses: (2x + 3)(x - 1).
- Type ^2 or ² to square a binomial: (3x - 4)².
- Any letters work: (a + b)(c + d).
- Two variables work too: (x + y)(x - y).
- Select Clear to start a new problem.
How to Multiply Binomials
To multiply two binomials, multiply each term in the first binomial by each term in the second. That gives four products. Add them and combine like terms.
This is the distributive property applied twice: a(c + d) + b(c + d). The FOIL method is a memory aid for the same four products.
How the Multiply Binomials Calculator Works
Here are the steps for (2x + 3)(x − 1):
- Distribute 2x: 2x · x = 2x² and 2x · (−1) = −2x.
- Distribute 3: 3 · x = 3x and 3 · (−1) = −3.
- Combine like terms: −2x + 3x = x.
- Write the answer in standard form: 2x² + x − 3.
Special Binomial Products
Three patterns come up often enough to memorize:
| Pattern | Formula | Example |
|---|---|---|
| Square of a sum | (a + b)² = a² + 2ab + b² | (x + 4)² = x² + 8x + 16 |
| Square of a difference | (a − b)² = a² − 2ab + b² | (3x − 4)² = 9x² − 24x + 16 |
| Difference of squares | (a + b)(a − b) = a² − b² | (x + 5)(x − 5) = x² − 25 |
A common mistake is writing (x + 4)² as x² + 16. The middle term 2ab is easy to forget. See more common FOIL mistakes.
Multiply Binomials Examples
| Problem | Answer | Note |
|---|---|---|
| (x + 2)(x + 5) | x² + 7x + 10 | 5x + 2x = 7x |
| (2x + 3)(x − 1) | 2x² + x − 3 | −2x + 3x = x |
| (x + y)(x − y) | x² − y² | The xy terms cancel |
| (3x + 2y)(x − y) | 3x² − xy − 2y² | −3xy + 2xy = −xy |
| (a + b)(c + d) | ac + ad + bc + bd | No like terms to combine |
Multiply Your Next Pair of Binomials
Multiply every term by every term, then combine like terms. Try the multiply binomials calculator above, see the same product as a grid with the box method calculator, or factor it back with the reverse foiling calculator.
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