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# 10 Examples of the Distributive Property

September 20, 2023
written by Rida Mirza

The distributive property is a fundamental concept in mathematics that helps simplify expressions and equations. It plays a important role in algebra and serves as a building block for more complex mathematical operations.

In this article, we will discuss 10 Examples of the Distributive Property in math, understanding its applications and significance.

## Examples of the Distributive Property

These are 10 examples of distributive property.

### 1: Understanding the Distributive Property

The distributive property states that for any real numbers ‘a,’ ‘b,’ and ‘c,’ the expression ‘a(b + c)’ is equal to ‘ab + ac.’

### 2: Distributive Property with Numbers

For example, 3(2 + 5) can be simplified as 32 + 35, which equals 6 + 15, resulting in 21.

### 3: Distributive Property with Variables

In algebra, the distributive property applies to variables as well. For example, 2(x + y) can be expanded to 2x + 2y.

### 4: Factoring with the Distributive Property

The distributive property can be used in reverse to factor expressions. For example, in 6x + 12, we can factor out 6, resulting in 6(x + 2).

### 5: Distributive Property in Algebraic Expressions

The distributive property simplifies complex algebraic expressions like (a + b)(x – y), which can be expanded as ax – ay + bx – by.

### 6: Distributive Property in Geometry

In geometry, the distributive property is used to find the area of complex shapes by breaking them into simpler parts.

### 7: Distributive Property in Linear Equations

Linear equations often involve the distributive property to solve for unknown variables. For instance, 3(x + 4) = 21 can be solved by distributing 3 and then isolating ‘x.’

### 8: Distributive Property in Polynomial Expressions

In polynomial expressions, the distributive property allows us to multiply each term of one polynomial by each term of another.

### 9: Distributive Property in Real-Life Scenarios

The distributive property can be applied to real-life scenarios, such as calculating the total cost of items with different prices and quantities.

### 10: Advanced Applications of the Distributive Property

Advanced mathematics, including calculus and linear algebra, use the distributive property as a foundational concept in more complex operations.

The distributive property is a powerful mathematical concept that simplifies expressions and equations, making complex mathematics more accessible.

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