Why is it called the 'distributive' property?

The word distribute means to spread or share. Here, the number outside the parentheses gets spread or distributed to every term inside the parentheses. Each term receives the multiplication, so nothing gets left out.

Does Distributive Property work with subtraction?

Yes. Treat subtraction as adding a negative: a(b - c) = a(b + (-c)) = ab - ac. The key is to remember that the negative sign distributes too, so -2(3 - 5) = -2 \cdot 3 + (-2) \cdot (-5) = -6 + 10 = 4.

What is the difference between Distributive Property and Order of Operations?

Order of Operations (PEMDAS) tells you the sequence in which to evaluate any expression. Distributive Property is a specific technique to remove parentheses by multiplying a term across a sum. When an expression has only numbers, you can use Order of Operations directly: compute inside parentheses first, then multiply. But when variables are present, like 3(x + 2), you cannot simplify the parentheses, so Distributive Property is essential.

Can I use Distributive Property if the parentheses contain multiplication or division?

No. Distributive Property works only when the parentheses contain addition or subtraction. For example, 3(2 + 5) uses it, but 3(2 \cdot 5) does not—you would just follow Order of Operations directly: 3 \cdot 2 \cdot 5 = 30. Multiplication and division do not distribute the same way.

Distributive Property

The Distributive Property lets you multiply a number by a sum or difference by distributing the multiplication to each term separately.

a(b + c) = ab + ac

Solve a problem with Distributive Property

Type the problem. The solver will use Distributive Property where Distributive Property is the right tool, and tell you when it is not.

What each symbol means

What Distributive Property takes

Symbol	Meaning
$a$	A number (called the multiplier) that sits outside the parentheses and gets distributed to every term inside; if a is negative, the sign distributes too.
$b$	The first term inside the parentheses; it is added to or subtracted from c, and will be multiplied by a.
$c$	The second term inside the parentheses; it is added to or subtracted from b, and will also be multiplied by a.

When to use it

Reach for Distributive Property whenever you need to remove parentheses from an expression like a(b + c) or when you want to simplify an expression that has a number multiplying a sum or difference.

Level

Usually taught in: Pre-Algebra

Worked examples

1. Expand a simple product with positive integers

Problem

Expand

3(2 + 5)

$3(2 + 5) = 3 \cdot 2 + 3 \cdot 5$
We distribute the 3 to both the 2 and the 5, multiplying each term separately.
$6 + 15$
We calculate $3 \cdot 2 = 6$ and $3 \cdot 5 = 15$ .
$21$
Finally, we add: $6 + 15 = 21$ .

Answer: $21$

Distributive Property lets us avoid computing what is in the parentheses first. Instead, we multiply 3 by each term inside, then add the products. Both methods give the same answer—this way is clearer for problems with variables.

2. Distribute across a subtraction with a variable term

Problem

Expand

5(2x - 3)

$5(2x - 3) = 5 \cdot 2x + 5 \cdot (-3)$
We distribute the 5 to both the $2x$ term and the $-3$ term, treating subtraction as addition of a negative.
$10x + (-15)$
We calculate $5 \cdot 2x = 10x$ and $5 \cdot (-3) = -15$ .
$10x - 15$
We simplify $10x + (-15)$ to $10x - 15$ . The Distributive Property has fully expanded the expression.

Answer: $10x - 15$

When variables are present, we cannot simplify what is inside the parentheses, so Distributive Property is essential. We must distribute the 5 to every term, including the constant, so that the expression expands completely.

3. Apply Distributive Property to a basketball scoring problem

Problem

A basketball player makes three-pointers in two games. In game 1, they make 5 three-pointers. In game 2, they make 4 three-pointers. Use the Distributive Property to find the total points scored from three-pointers across both games.

$3(5 + 4) = 3 \cdot 5 + 3 \cdot 4$
We distribute the point value 3 to each game: $3 \cdot 5$ for game 1's three-pointers, plus $3 \cdot 4$ for game 2's.
$15 + 12$
We calculate the points per game: $3 \cdot 5 = 15$ points from game 1, and $3 \cdot 4 = 12$ points from game 2.
$27$
We add the two games' totals: $15 + 12 = 27$ points.

Answer: $27 \text{ points}$

This problem shows why Distributive Property is useful in real life. Rather than adding the three-pointers first ( $5 + 4 = 9$ ) then multiplying by 3, we can distribute the 3 to each game and add the results. Both paths give 27 points, but Distributive Property matches how the problem is structured: one action (3 points per three-pointer) applied to two groups.

Common mistakes

Where Distributive Property usually goes wrong

The mistake	Why it is wrong	The fix
$3(2 + 5) = 3 \cdot 2 + 5$	The 3 only multiplied the first term; it must distribute to both the 2 and the 5.	$3(2 + 5) = 3 \cdot 2 + 3 \cdot 5 = 6 + 15 = 21$
$-2(3 - 4) = -6 - 4 = -10$	The negative sign distributes to both terms, so when $-2$ multiplies $-4$ , the result is positive 8, not $-4$ .	$-2(3 - 4) = (-2)(3) + (-2)(-4) = -6 + 8 = 2$
$2(x + 3) = 2x + 3$	The 2 only multiplied the variable x; it must also multiply the constant 3.	$2(x + 3) = 2x + 2 \cdot 3 = 2x + 6$

Tips and when to use something else

Count the terms inside the parentheses and make sure you distribute to every one. For longer expressions like $3(a + b + c)$ , distribute to all three terms: $3a + 3b + 3c$ .
Distributive Property is the reverse of factoring. If you can factor out a common number from a sum—like seeing $6 + 9 = 3(2 + 3)$ —you understand both directions of the same idea.
Use Distributive Property for mental math by breaking hard numbers into simpler pieces. For example, $7 \times 13 = 7(10 + 3) = 70 + 21 = 91$ is often easier than computing $7 \times 13$ directly.
When you see a negative sign in front of parentheses, like $-(a + b)$ , think of it as $-1(a + b) = -a - b$ . This helps you remember that the negative distributes to every term inside.

Related formulas

Order of OperationsOrder of Operations is the set of rules that tells you which calculation to do first when you have multiple operations in one expression.Commutative PropertyThe Commutative Property says you can switch the order of numbers when adding or multiplying without changing the result.Associative PropertyGrouping numbers differently in addition doesn't change the sum, so you can rearrange parentheses to make calculations easier or more convenient.Greatest Common FactorThe Greatest Common Factor finds the largest whole number that divides evenly into two or more numbers, helping you simplify fractions.

Frequently asked questions

Why is it called the 'distributive' property?: The word distribute means to spread or share. Here, the number outside the parentheses gets spread or distributed to every term inside the parentheses. Each term receives the multiplication, so nothing gets left out.
Does Distributive Property work with subtraction?: Yes. Treat subtraction as adding a negative: $a(b - c) = a(b + (-c)) = ab - ac$ . The key is to remember that the negative sign distributes too, so $-2(3 - 5) = -2 \cdot 3 + (-2) \cdot (-5) = -6 + 10 = 4$ .
What is the difference between Distributive Property and Order of Operations?: Order of Operations (PEMDAS) tells you the sequence in which to evaluate any expression. Distributive Property is a specific technique to remove parentheses by multiplying a term across a sum. When an expression has only numbers, you can use Order of Operations directly: compute inside parentheses first, then multiply. But when variables are present, like $3(x + 2)$ , you cannot simplify the parentheses, so Distributive Property is essential.
Can I use Distributive Property if the parentheses contain multiplication or division?: No. Distributive Property works only when the parentheses contain addition or subtraction. For example, $3(2 + 5)$ uses it, but $3(2 \cdot 5)$ does not—you would just follow Order of Operations directly: $3 \cdot 2 \cdot 5 = 30$ . Multiplication and division do not distribute the same way.

Need a different method?

The full solver is not scoped to one formula — type any problem and it will pick the method.

Open the math solver

Reviewed 2026-09-18