Last updated on July 5th, 2025
The distributive property of multiplication states that multiplying a number by a sum gives the same result as multiplying each addend separately and then adding the products. This property applies to both addition and subtraction. In this article, we will discuss its formula, applications, and significance.
The distributive property is multiplying a number by sum equals to multiplying the number by each addend separately and then adding the products. It breaks down and simplifies expressions. To distribute anything is to divide or assign a portion of something. We apply this property to describe the way by which multiplication extends to addition and subtraction.
Distributive Property of Multiplication Formula
Using the distributive property of multiplication, we solve an expression of the form A(B + C) by expanding it as:
A(B + C) = AB + AC
This property also applies to subtraction:
A(B – C) = AB – AC
where A, B, and C are any real numbers.
Distributive Property of Multiplication Over Addition
The distributive property of multiplication shows that when the sum is multiplied by another number, each term in the sum can be multiplied individually by that number, and the results can then be added together for the same outcome. Consider the example: 5(6 + 4) by expanding it:
5(6 + 4) = 5(6) + 5(4) = 30 + 20 = 50
Here, we distribute the numbers 5 to both 6 and 4 and then sum up their products separately.
Using BODMAS rule also gives the same result
5 (6 + 4) = 5 (10) = 50
As both methods give the same result, the distributive property is true.
Distributive property of multiplication over subtraction
The distributive property of multiplication over subtraction states that you can multiply a number by each value separately and subtract the results. This is the same as multiplying the number by the difference between the two values. The formula we use for the distributive property of multiplication over subtraction is:
a(b – c) = ab – ac.
For example:
Solve 7 (15 – 5) using both methods:
As per this property, the result on both LHS and RHS is the same.
On the left-hand side (LHS), we evaluate directly:
7 (15 – 5) = 7 (10) = 70
In RHS, we apply the distributive property:
7 × 15 – 7 × 5 = 105 – 35 = 70
Since both sides give the same result, we confirm that the property holds.
Understanding the distributive property enhances students' ability to simplify complex calculations. It applies not only to math but also to real life. Some real-life applications are:
Mostly, students make mistakes in calculating the sum and product of the numbers. Here are a few common mistakes and ways to avoid them:
Solve 8 (9 + 6) using the distributive property.
8 (9 + 6) = 120
Apply the distributive property formula:
A (B + C) = AB + AC
Using the distributive property, distribute the number 8 to both terms within the brackets.
8 (9 + 6) = 8 × 9 + 8 × 6
Now, multiply the terms:
72 + 48 = 120
So, 8 (9 + 6) = 120.
Expand 6 (y + 5) using the distributive property.
6 (y + 5) = 6y + 30.
We apply the distributive property to expand the expression:
A (B + C) = AB + AC
Substituting the given values:
6 (y + 5) = 6 × y + 6 × 5
Now, simplify the expression:
6y + 30
So, 6 (y + 5) = 6y + 30.
Solve - 4 (10 – 2) using the distributive property.
-4(10 –2) = –32
To solve this expression, we apply the distributive property:
–4 (10 – 2) = –4 × 10 + (–4) × (-2)
Now, multiply the terms:
–40 + 8 = –32
So, –4(10 –2) = –32.
Solve 12 (5 + 7 - 6) using the distributive property.
12 (5 + 7 - 6) = 72
We first simplify inside the brackets:
5 + 7 – 6 = 6
Now, we apply the distributive property:
12 (6) = 12 × 6 = 72
So, 12 (5 + 7 - 6) = 72.
Solve 3(x - 6) using the distributive property.
3(x - 6) = 3x - 18
Apply the distributive property of multiplication:
A (B - C) = AB - AC
We have: A = 3, B = x, and C = 6.
Now distribute 3 to both terms inside the parentheses:
3 (x - 6) = 3 × x - 3 × 6
Multiply the terms:
3x - 18
So, 3(x - 6) = 3x - 18.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.