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Chapter 7: Problem 106

In the following exercises, simplify using the distributive property. $$r(s-18)$$

Short Answer

Expert verified
rs - 18r

Step by step solution

01

Identify the terms inside the parentheses

The expression inside the parentheses is \(s-18\). This will help in applying the distributive property correctly.
02

Apply the distributive property

To apply the distributive property, multiply \(r\) by each term inside the parentheses: Multiply \(r\) by \(s\) to get \(r \times s\). Then, multiply \(r\) by \(-18\) to get \(r \times -18\).
03

Execute the multiplication

Perform the multiplication: \(r \times s = rs\) and \(r \times -18 = -18r\). Now combine these results to get the simplified expression.
04

Combine the terms

Combine the terms to form the final simplified expression: \(rs-18r\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplification
Simplification in algebra involves reducing expressions to a simpler form. The goal is to make complex expressions easier to work with and understand. It often involves combining like terms and applying algebraic properties like the distributive property.
When simplifying, follow these steps:
  • Identify the terms in the expression
  • Apply algebraic rules like the distributive property
  • Combine like terms

In our example, we start with the expression \(r(s - 18)\). Applying the distributive property allows us to simplify it to \(rs - 18r\).
Multiplication
Multiplication in algebra is combining two quantities to get a product. When dealing with algebraic expressions, we follow certain rules to multiply variables and numbers.
Here鈥檚 how to multiply algebraic expressions:
  • Multiply the coefficients (numbers) together
  • Multiply the variables together. If they are the same, combine them using exponents

In the expression \(r(s - 18)\), we multiply \(r\) by each term inside the parentheses. This results in \(r \times s = rs\) and \(r \times -18 = -18r\).
The final step involves combining these products.
Algebraic Expressions
An algebraic expression is a combination of numbers, variables, and operators (such as +, -, \(\times\), and \(\div\)). They represent mathematical relationships and can be simplified or manipulated using algebraic rules.
  • Terms in an expression are the individual parts separated by + or - signs
  • A variable is a symbol, often a letter, that represents a number
  • Coefficients are the numerical part of the terms

In our example, \(r(s - 18)\) is an algebraic expression where \(r \) and \( s \) are variables. The distributive property helps us break down and simplify this expression to \( rs - 18r \). This simpler form is easier to understand and work with.

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