Distributive property calculator
Enter three numbers and watch 3(4 + 5) become 3·4 + 3·5, then 12 + 15, then 27. Each step of the distributive property is shown next to the answer, so a student can check the working, not just the result. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- A
- 3
- B
- 4
- C
- 5
- Value
- 27
- Original
- 3(4 + 5)
- Expanded
- 3*4 + 3*5
- Term ab
- 12
The distributive property says that a times the sum of b and c equals the sum of a times b and a times c. Every algebra course introduces a(b + c) as the first expansion students must write without dropping a sign, and the same identity is how mental arithmetic, spreadsheet formulas, and compiler folding multiply through a parenthesis. This calculator accepts the three finite numbers a, b, and c, echoes the grouped original, expands it by multiplying a through both addends, and returns the numeric value of the result.
What a(b + c) means and how the two products appear
The distributive property of multiplication over addition is the identity a(b + c) equals a times b plus a times c. A factor sitting outside a pair of parentheses multiplies every term inside those parentheses, and the products are then added.
That single rule is how algebra students expand three times the quantity x plus two into three x plus six, how a shopkeeper computes four items at two fifty plus four items at one twenty-five without adding the unit prices first, and how a compiler rewrites constant arithmetic before emitting code. This capability specialises the identity to three finite numbers: you supply a, b, and c, and it returns both the expanded writing a times b plus a times c and the evaluated value.
The original grouped form is echoed as a display string so a learner can see three times the quantity four plus five next to three times four plus three times five next to twenty-seven. Negatives are first-class citizens: three times the quantity four plus negative five still distributes as three times four plus three times negative five, which equals twelve plus negative fifteen, which equals negative three.
Zero is allowed in any slot; zero times the quantity b plus c expands to zero times b plus zero times c and evaluates to zero, which is a useful check that the implementation did not skip a factor. Because multiplication of real numbers is associative and commutative, the value of a(b + c) always equals the value of ab plus ac; the calculator still shows both the expanded writing and the number so students can match textbook steps rather than only the final answer.
The algorithm is a handful of arithmetic operations with no symbolic engine, no network, and no randomness, so the same three numbers always produce the same strings and the same value. The capability does not expand a(b + c + d), does not treat subtraction as a separate operator (subtraction is addition of a negative), and does not factor a sum back into a product; those are different search intents.
Where a distributive property calculator earns its keep
Classrooms and tutoring platforms use a distributive property calculator so learners can check that they multiplied the outer factor through both addends without dropping a sign. Exam generators and learning-management graders need a deterministic oracle that marks a non-numeric coefficient as invalid instead of silently coercing it to zero, which would award a false pass. Failed validation does not consume balance.
Pin the expanded string and the value in tests, and you get reproducible results for homework, LMS plugins, and edge workers without standing up symbolic math infrastructure of your own. The capability does not solve for an unknown factor, does not expand binomials of higher degree, and does not multiply two polynomials of arbitrary length; those are different search intents served by other catalog entries such as a binomial expansion or a polynomial multiply tool.
Keep requests small, treat the display strings as contract, and you have a stable oracle for the first identity every algebra course teaches.
What you can do with it
Classroom and homework checks
Let students submit a, b, and c for a(b + c) and verify the expanded writing a*b + a*c plus the numeric value against textbook steps.
Exam and LMS auto-grading
Mark distributive-property items with a deterministic oracle that rejects non-finite coefficients instead of coercing them to zero.
Scaled sums in notebooks and prices
Compute an outer factor times two addends in rate, tax, and unit-price scripts without importing a computer-algebra library.
FAQ
What happens if a, b, or c is not a finite number?
Missing, empty, infinite, and non-numeric values are rejected and are not billed.
Does the calculator handle negative numbers?
Yes. Negatives are valid finite numbers. Negative factors are wrapped in parentheses in original and expanded so a leading minus is unambiguous.
What does the calculator show besides the final answer?
It shows the grouped form you started with, the expanded form with both products, each product on its own and the value. With 3, 4 and 5 you see 3(4 + 5), 3·4 + 3·5, 12, 15 and 27.
Can I use zero in the distributive property?
Yes, in any of the three places. A zero outside the parentheses expands to zero times each number inside and the value is 0, a quick way to confirm that no factor was skipped.
How do I distribute over a subtraction?
Write it as adding a negative number. 3(4 + −5) expands to 3·4 + 3·(−5), which is 12 + (−15), so the value is −3. Negative numbers appear in parentheses so the sign is never ambiguous.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/math/distributive-property-old \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"a":3,"b":4,"c":5}'const res = await fetch("https://api.kit.forhosting.com/math/distributive-property-old", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"a": 3,
"b": 4,
"c": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/math/distributive-property-old",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"a": 3,
"b": 4,
"c": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/math/distributive-property-old", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"a":3,"b":4,"c":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"a":3,"b":4,"c":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/math/distributive-property-old", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"a": 3,
"b": 4,
"c": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "math.distributive_property_old",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Missing, empty, infinite, or non-numeric fields fail with invalid_input and are not billed, so graders never confuse a NaN with a real product.
Input contract, response shape, and error behaviour
Negative factors are wrapped in parentheses in the display strings so a leading minus is never ambiguous. POST a JSON body with three required finite numbers: a, the factor outside the parentheses; b, the first addend inside; and c, the second addend inside. Each field may arrive as a JSON number or as a numeric string; non-finite values, missing fields, empty strings, and values that do not parse as numbers fail with invalid_input naming the field. Those failures are not billed. On success the body echoes the cleaned coefficients a, b, and c; original, a display string of the grouped form such as three times the quantity four plus five; expanded, a display string of the distributed products such as three times four plus three times five; term_ab and term_ac, the two individual products; value, the finite numeric result of a times b plus a times c; and formula, the identity a(b + c) equals a times b plus a times c. Example: a equals three, b equals four, c equals five yields original 3(4 + 5), expanded 3*4 + 3*5, term_ab twelve, term_ac fifteen, and value twenty-seven. Example: a equals two, b equals negative three, c equals five yields original 2((-3) + 5), expanded 2*(-3) + 2*5, term_ab negative six, term_ac ten, and value four. If a product or the final sum overflows IEEE floating-point to Infinity or NaN, the task fails with invalid_input rather than returning a non-finite success payload. Pair the response with your own typesetting if you need a rendered multiplication dot; this endpoint computes the expansion and the number only and does not emit plots or step-by-step prose beyond the formula field.
Where a distributive property calculator earns its keep
Engineering notebooks, finance spreadsheets, and unit-price calculations call a(b + c) constantly: combined rates, tax-plus-fee totals, and scaled sums all reduce to one outer factor times two addends, and a tiny parse API avoids pulling a computer-algebra system for three numbers.
Technical questions
How do I expand a(b + c) with the distributive property?
Send finite numbers a, b, and c. The API returns original a(b + c), expanded a*b + a*c, the two products term_ab and term_ac, and value equal to a*b + a*c.
What fields does a successful call return?
The cleaned inputs a, b, and c; original and expanded display strings; term_ab and term_ac; value; and the formula a(b + c) = a*b + a*c.
What does the distributive property calculator cost?
The browser tool is free. API requests use prepaid balance at $0.002 per successful call; invalid input is not billed.