The Distributive Property

Definition and Application

The distributive property is a fundamental property of real numbers used to simplify expressions and solve equations. It states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the results.

• General Form: For any real numbers a, b, and c:

• This property is used to remove parentheses in algebraic expressions.

• It applies to both addition and subtraction inside the parentheses.

Example Problem

Question: Multiply using the distributive property.

• Step 1: Distribute x to each term inside the parentheses:

• Step 2: Simplify each term:

• Final Answer:

Additional Examples

• Example 1:

• Example 2:

Key Points

• The distributive property helps simplify expressions and solve equations.

• Always multiply the term outside the parentheses by each term inside.

• Combine like terms if possible after distributing.