The Distributive Property: Simplify and Solve Algebraic Expressions with this Fundamental Math Concept

Distributive Property

The Distributive Property is a fundamental concept in mathematics used to simplify and solve algebraic expressions

The Distributive Property is a fundamental concept in mathematics used to simplify and solve algebraic expressions. It states that when we multiply a number or variable by a sum or difference inside parentheses, we can distribute the multiplication across each term individually.

The general form of the Distributive Property can be expressed as:

a(b + c) = ab + ac

Here, ‘a’ represents any number or variable, and ‘b’ and ‘c’ are terms inside the parentheses.

Let’s work through an example to help solidify this concept:

Example:

Simplify the expression 3(2x + 4).

Solution:

To simplify this expression using the Distributive Property, we will distribute the multiplication of 3 across each term inside the parentheses.

Starting with 3(2x), we can rewrite it as 3 * 2x, which simplifies to 6x.

Moving on to 3(4), we can rewrite it as 3 * 4, which simplifies to 12.

Now, we can combine the simplified terms to get the final answer:

6x + 12

So, the simplified expression for 3(2x + 4) is 6x + 12.

The Distributive Property can also be used in reverse to factor out common terms in an expression. Let’s work through another example for this case:

Example:

Factor out the common factor of 4 in the expression 4x + 4y.

Solution:

To factor out the common factor of 4, we can use the Distributive Property in reverse.

We start by writing 4 as the common factor outside of the parentheses: 4(x + y).

Now, we need to distribute 4 across each term inside the parentheses.

4(x) simplifies to 4x, and 4(y) simplifies to 4y.

Combining the simplified terms, we get the final factored expression:

4x + 4y = 4(x + y).

So, by applying the Distributive Property in reverse, we’ve factored out the common factor of 4 in the expression 4x + 4y.

In summary, the Distributive Property allows us to simplify or factor expressions by distributing the multiplication across each term inside parentheses. It is an important tool in algebra and helps us simplify equations and solve problems more efficiently.

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