Simplifying Algebraic Expressions With The Distributive Property: A Comprehensive Guide

Distributive Property

The sum of two addends multiplied by a number is the sum of the product of each addend and the number.

The distributive property is a mathematical property that explains how to distribute a common factor or term to each term or factor inside a set of parentheses. In other words, it is a way to simplify expressions by multiplying or dividing a number or variable to each term within a set of parentheses.

The distributive property can be expressed as:

a(b + c) = ab + ac

or

(a + b)c = ac + bc

In the first example, the common factor is a, and it is distributed to each term inside the parentheses, b and c. So, the expression a(b + c) can be simplified to ab + ac.

In the second example, the common factor is c, and it is distributed to each term inside the parentheses, a and b. So, the expression (a + b)c can be simplified to ac + bc.

The distributive property can also be applied to more complex expressions, such as:

2(a + 3b) – 4c

In this example, we can first distribute the 2 to each term inside the parentheses:

2(a + 3b) = 2a + 6b

And then, we can subtract 4c:

2a + 6b – 4c

So, the original expression can be simplified to 2a + 6b – 4c.

Overall, the distributive property is a powerful tool in simplifying and solving algebraic expressions, and it is a fundamental concept for students learning algebra.

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