Distributive Property Calculator
Interactive distributive property solver
Enter the outer multiplier and the expression inside parentheses. We’ll show each multiplication step.
Step-by-step solution
What is the distributive property?
The distributive property states: a(b + c) = ab + ac. It lets you multiply a sum by multiplying each addend separately and then adding the products. Essential for algebra, it removes parentheses and simplifies expressions.
Why use our 2026 calculator?
✔ Step-by-step breakdown ✔ Handles fractions & decimals ✔ Works with variables (x, y, z) ✔ Combine like terms automatically ✔ Perfect for homework, test prep, and quick verification.
Real-world applications
From calculating area of combined rectangles to mental math (7×98 = 7×(100-2)=700-14=686). Used in finance, construction takeoffs, and algebraic modeling.
Distributive property examples table
| Original expression | Distributed form | Simplified result |
|---|---|---|
| 5(3x + 2) | 5·3x + 5·2 | 15x + 10 |
| -2(4y - 7) | -2·4y + (-2)(-7) | -8y + 14 |
| ⅓(9x + 12) | ⅓·9x + ⅓·12 | 3x + 4 |
| 0.6(5x - 3) | 0.6·5x - 0.6·3 | 3x - 1.8 |
| 3(2x + 4y - 1) | 6x + 12y - 3 | 6x + 12y - 3 |
How to use the distributive property calculator (step by step)
- Enter the outer factor – can be integer, fraction (like 2/3), or decimal.
- Type the expression inside parentheses – e.g., "3x+5", "2y-7", "x+2y+3z".
- Click “Apply distributive property” – our solver multiplies each term by the outer factor.
- Read the step-by-step explanation – each multiplication is shown individually.
- Get final simplified expression – like terms automatically combined (e.g., 2x+3x → 5x).
2026 updated: supports fractional coefficients, negative numbers, and up to 5 terms inside parentheses.
Exclusive insights: 5 common mistakes & how to avoid them
−2(3x−4) → −6x +8 (not −6x−8). Always distribute the negative sign.
2(x+3) = 2x+6, not 2x+3. Distribute to EVERY term inside.
Multiply numerator × term, keep denominator. (2/3)(9x) = (18x/3)=6x.
Always simplify: 3x+2x =5x.
Distributive property works for any term: a(bx²) = abx².
Advanced use: distributive property with fractions & combining like terms
Our calculator excels at distributive property with fractions and also handles distributive property polynomials. For instance, entering outer factor "2/3" and inner "6x+9" produces (2/3*6x) = 4x and (2/3*9)=6, giving 4x+6. You can also use it to remove parentheses in multi-step equations. This is the perfect algebra distributive property calculator for middle school, high school, and college prep.
Checklist for solving equations using distributive property:
- ✅ Identify the term outside parentheses.
- ✅ Multiply each term inside by the outer factor (watch signs).
- ✅ Rewrite without parentheses.
- ✅ Combine any like terms that appear.
- ✅ Solve for variable if equation is given.
Frequently Asked Questions (distributive property)
Yes. It distributes to every term: 6x + 8y - 10z, and displays each multiplication step.
Absolutely. Enter fractions like 3/4 or decimals 2.5; the calculator shows exact multiplication results.
Yes! After distributing, it groups terms with the same variable and simplifies (e.g., 3x+5x becomes 8x).
Exactly. This tool simplifies expressions, perfect for solving equations like 2(x+3)=10. Use the result to continue solving.
FOIL is a specific case for (a+b)(c+d). Distributive property is broader: a(b+c) or a(b-c). Our tool covers basic and multi-term distribution.
Yes. It handles variable names and will multiply coefficients appropriately. Terms like 3x² are preserved.
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