Problem 94 - Beginning and Intermediate Algebra

Question

Write each expression without parentheses. $$ -(-13 x-15 y) $$

Step-by-Step Solution

Answer

13x + 15y

Step 1: Understand the Problem

Given expression contains parentheses with a negative sign outside: a. -(-13x - 15y)

Step 2: Distribute the negative sign

When distributing the negative sign across the parentheses, change the sign of each term inside the parentheses.b. -(-13x) - (-15y) = 13x + 15y

Step 3: Combine the results

Combine the simplified terms from the distribution to write the expression without parentheses.c. 13x + 15y

Key Concepts

Simplifying Algebraic Expressions

Simplifying algebraic expressions means making them easier to work with. Let's take the exercise example as a starting point. You have the expression oooooo expression contains parentheses and a negative sign outside. To simplify it: Distribute the negative sign to each term inside the parentheses. By changing the sign of each term inside the parentheses, the expression becomes easier to read and use.

Parentheses in Algebra

Parentheses in algebra are used to group terms and indicate which parts of the expression should be dealt with first. The given example illustrates this well: oo when needed. For example, in oo The negative sign in front of the parentheses can be tricky. Distributing the negative sign correctly ensures proper simplification.

Basic Algebra Operations

Basic algebra operations include addition, subtraction, multiplication, and division. Understanding these operations is crucial for solving algebra problems. Let's prepare for our given example:

• Addition and subtraction: Combining like terms or changing signs
• Multiplication: Distributing factors across terms
• Division: Dividing terms individually

In our exercise, the main operation is distributing or 'multiplying' the negative sign over the terms in the parentheses. This changes each term's sign from negative to positive or vice versa: