Math
Distributive Property Calculator
Type the two factors of a product, for example 3 and 2x - 5, or x + 3 and x - 5, and the calculator multiplies every term of the first by every term of the second, lists the partial products in order, and combines like terms into the expanded form.
Purely numeric inputs such as 7 and 40 + 6 show the mental-math split 7 × 46 = 280 + 42 = 322. Variables can be any single letters, so (2a + b)(a - 3b) works too.
A number, a single term like -2x, or a sum like x + 3. Single-letter variables, optional ^ powers (x^2).
The sum (or difference) being distributed over. Up to 6 terms in each factor.
Try an example
Result
Expanded form
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- Partial products
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- Original expression
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- Terms before combining
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- Check
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Study path
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What the distributive property calculator solves
The distributive property says that multiplying a number by a sum is the same as multiplying it by each addend and adding the results: a(b + c) = ab + ac. It is the rule behind mental multiplication (7 × 46 = 7 × 40 + 7 × 6), behind expanding algebraic expressions like 3(2x - 5) = 6x - 15, and, applied twice, behind multiplying binomials (FOIL). This calculator performs the expansion for any two factors and shows each partial product.
| Expression | Partial products | Expanded |
|---|---|---|
| 7(40 + 6) | 280 + 42 | 322 |
| 3(2x - 5) | 6x - 15 | 6x - 15 |
| -2(x + 4) | -2x - 8 | -2x - 8 |
| (x + 3)(x - 5) | x^2 - 5x + 3x - 15 | x^2 - 2x - 15 |
| (2a + b)(a - 3b) | 2a^2 - 6ab + ab - 3b^2 | 2a^2 - 5ab - 3b^2 |
| (x + 2)(x^2 - 2x + 4) | x^3 - 2x^2 + 4x + 2x^2 - 4x + 8 | x^3 + 8 |
Signs and negatives
The factor outside multiplies every term inside, sign included. -2(x + 4) = -2x - 8, and 3(2x - 5) = 6x - 15 because 3 × (-5) = -15. A minus sign in front of parentheses is a factor of -1: -(x - 7) = -x + 7. Writing the partial products with their signs before combining avoids most sign errors.
FOIL and beyond
For two binomials, FOIL (First, Outer, Inner, Last) is just the distributive property applied to each term of the first factor. With more terms there are more products (a trinomial times a binomial gives 6), and the same rule applies: every term times every term, then combine like terms. The calculator labels the four FOIL products when both factors are binomials and numbers them otherwise.
How to use it
- Type the first factor (a number, a term, or a sum) and the second factor (the sum to distribute over).
- Read the expanded form and the list of partial products.
- Open Show the work to see each product with its sign, the sum before combining, and the like-term step.
- For numeric inputs, use the check line to confirm the split matches direct multiplication.
How to read the answer
The expanded form is the product with no parentheses and like terms combined, written in descending powers. The partial products are the individual term-by-term multiplications; their count equals (terms in the first factor) × (terms in the second). For numeric inputs the check evaluates both sides; for algebraic inputs a spot check substitutes 2 for every variable.
Common mistakes and edge cases
- Multiplying only the first term inside the parentheses: 3(2x - 5) is 6x - 15, not 6x - 5.
- Dropping the sign of a negative factor: -2(x + 4) = -2x - 8, not -2x + 8.
- Adding instead of multiplying the outside factor: 3(x + 4) is not x + 7.
- Forgetting the Outer and Inner products when multiplying binomials: (x + 3)(x - 5) ≠ x^2 - 15.
- Combining unlike terms such as x^2 and x, or ab and a^2.
Worked examples
3(2x - 5)
6x - 15.
Expanded form
6x - 15
Mental math 7 × 46
7(40 + 6) = 280 + 42 = 322.
Expanded form
322
Negative factor
-2(x + 4) = -2x - 8.
Expanded form
-2x - 8
Binomial times binomial
(x + 3)(x - 5) = x^2 - 2x - 15.
Expanded form
x^2 - 2x - 15
Two variables
(2a + b)(a - 3b) = 2a^2 - 5ab - 3b^2.
Expanded form
2a^2 - 5ab - 3b^2
Sum of cubes pattern
(x + 2)(x^2 - 2x + 4) = x^3 + 8.
Expanded form
x^3 + 8
Decimal coefficient
0.5(4x + 6) = 2x + 3.
Expanded form
2x + 3
Unreadable factor
Words are rejected.
Expanded form
Error
Frequently asked questions
What is the distributive property?+
a(b + c) = ab + ac: multiplying a sum by a number is the same as multiplying each part and adding. 3(2x - 5) = 6x - 15.
How do I distribute a negative number?+
Multiply every term by it, keeping track of signs: -2(x + 4) = -2x - 8 and -2(x - 4) = -2x + 8.
Is FOIL the same as the distributive property?+
Yes. FOIL is the distributive property applied twice to two binomials: (a + b)(c + d) = ac + ad + bc + bd.
How do I use the distributive property for mental math?+
Split one factor into easy pieces: 7 × 46 = 7 × 40 + 7 × 6 = 280 + 42 = 322, or 8 × 99 = 8 × 100 - 8 × 1 = 792.
What happens with more than two terms?+
Multiply every term of one factor by every term of the other. A binomial times a trinomial gives 6 products before combining like terms.
Can I distribute over subtraction?+
Yes: a(b - c) = ab - ac, because b - c is b + (-c).
What is the reverse of distributing?+
Factoring: 6x - 15 = 3(2x - 5) pulls the common factor back out.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026