/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 Use the distributive property to... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 69

Use the distributive property to write each sum as a product. See Example 5 \(30 a+30 b\)

Short Answer

Expert verified
The expression is factored as \(30(a + b)\).

Step by step solution

01

Identify the Common Factor

Look at the expression \(30a + 30b\). Notice that 30 is a common factor in both terms, \(30a\) and \(30b\). This means we can factor out a 30 from each term.
02

Apply the Distributive Property

By applying the distributive property, we factor out the common factor (30) from each term of the sum. This is done by writing the expression as a product of the common factor and a sum of the remaining terms inside parentheses: \(30(a + b)\).
03

Verify the Factoring

To ensure the expression is correctly factored, distribute the 30 across the terms inside the parentheses. Re-distributing gives \(30 \times a + 30 \times b\), which simplifies to the original expression \(30a + 30b\), confirming that \(30(a + b)\) is the correct factored form.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Factoring Expressions
Factoring expressions is a fundamental skill in algebra that involves rewriting an expression as a product of its factors. Think of it like splitting a number into its building blocks. This can make complex problems easier to solve by simplifying expressions.When you factor an expression, you aim to identify a common factor that each term shares. Once found, you "pull out" this factor, which means you divide each term by this factor and factor it out of the expression.
  • For instance, in the expression \(30a + 30b\), both terms have the common factor 30.
  • Factoring results in a simpler form, \(30(a + b)\), which is often more useful for solving equations or simplifying mathematical problems.
Factoring is essential because it reduces expressions and reveals deeper arithmetic properties. It's a key step in solving problems and understanding the structure of algebraic expressions.
Algebraic Expressions
Algebraic expressions use numbers, variables, and arithmetic operations (like addition and multiplication) to represent mathematical ideas. They allow you to generalize things like mathematical relationships and are fundamental in solving equations.In an algebraic expression, the variables stand in for unknown values. For example, \(a\) and \(b\) in \(30a + 30b\) could be any numbers.
  • Algebraic expressions are versatile and used extensively in every aspect of algebra, often needing to be simplified or factored.
  • They serve as the foundation for understanding more complicated concepts, equations, and functions in math.
Understanding algebraic expressions involves knowing how to manipulate and simplify them using properties like the distributive property. This flexibility is what makes algebra such a powerful tool in mathematics and problem-solving.
Common Factor
A common factor refers to a number or variable that divides each term in an expression without a remainder. Finding a common factor is a crucial step in simplifying algebraic expressions by factoring. In our example, the expression \(30a + 30b\) has a common factor of 30:
  • The term \(30a\) can be divided by 30, leaving \(a\).
  • The term \(30b\) can be divided by 30, leaving \(b\).
  • Thus, the expression can be rewritten in its factored form as \(30(a + b)\).
Recognizing the common factor allows you to simplify expressions effectively. Identifying and factoring out the common factor streamlines solving and analyzing solutions in algebra.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify each expression. (Remember the order of operations.) See Examples 4 and 5. $$ 2-3(8-6) $$

Pythagoras died in the year \(-475\) (or 475 B.C.). When was he born, if he was 94 years old when he died?

Perform the following operations. Write answers in lowest terms. $$ \frac{7}{18} \div \frac{14}{36} $$

In some card games, it is possible to have a negative score. Lavonne Schultz currently has a score of 15 points. She then loses 24 points. What is her new score?

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. The difference of sixteen and four is greater than ten.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.