Distribute across parentheses with transparent, stepwise algebra. Expand variable terms cleanly, then merge exact like terms. Handle integers, fractions, or decimals with optional sorting. Export results instantly as CSV or PDF. Preview LaTeX formatting examples. Practice with examples, verify work, and learn every session.
a(b + c + …) = ab + ac + …
Multiply the outside factor with each term inside parentheses, then combine like terms. Variable parts multiply by concatenation, e.g., 2a × 3x = 6ax.
Supported: letters a–z; integer, fractional, or decimal coefficients; plus and minus signs. Variables are concatenated on multiplication and matched exactly for like-term combining.
| # | Multiplier | Expression | Options | Expanded & Simplified |
|---|---|---|---|---|
| 1 | 3a | 2x-5y+4 | combine, sort, frac | 6ax - 15ay + 12a |
| 2 | -2 | 5m-3n+7 | combine, sort | -10m + 6n - 14 |
| 3 | 1/2b | -x+y-2 | combine, sort, frac | -1/2bx + 1/2by - b |
| 4 | 2.5c | 3p+2q-1 | combine, frac | 7.5cp + 5cq - 2.5c |
Two worked examples show the step-by-step distribution and simplification.
Input: Multiplier 3a, Expression (2x - 5y + 4)
Result: 6ax - 15ay + 12a
Input: Multiplier 1/2b, Expression (-x + y - 2)
Result: -1/2bx + 1/2by - b
| Term A | Term B | Variable Parts | Combine? | Reason |
|---|---|---|---|---|
| 4ax | -7xa | ax vs ax | Yes | Identical letters |
| 3ab | 5ba | ab vs ab | Yes | Order normalized |
| 2a | -5a | a vs a | Yes | Same variable |
| 6ab | 3abc | ab vs abc | No | Different variables |
| 7x | 7x^2 | x vs xx | No | Different exponents |
| Multiplier | Term Sign | Product Sign | Example |
|---|---|---|---|
| + | + | + | 3a × 2x = +6ax |
| + | - | - | 3a × -5y = -15ay |
| - | + | - | -2b × 4m = -8bm |
| - | - | + | -2b × -3n = +6bn |
Negative outside the parentheses flips every term inside.
| # | Input Multiplier | Input Expression | Options | Expected Simplified Result |
|---|---|---|---|---|
| 1 | -3b | 4x-5y+7 | combine, sort | -12bx + 15by - 21b |
| 2 | 1/2a | 6m-3n+8 | combine, sort, frac | 3am - 3/2an + 4a |
| 3 | 2.5c | -x+y-2 | combine, frac | -2.5cx + 2.5cy - 5c |
| 4 | -5 | 3p+2q-1 | combine | -15p - 10q + 5 |
Use these to verify consistency across CSV export or LaTeX preview.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.