Problem 67 Use the distributive law to fact... [FREE SOLUTION]

91影视

Chapter 1: Problem 67

Use the distributive law to factor each of the following. Check by multiplying. $$ 2 a+2 b $$

Short Answer

Expert verified

\[ 2(a + b) \]

Step by step solution

Identify the common factor

Look at the terms provided, which are 2a and 2b. Identify the common factor in both terms.

Factor out the common factor

The number 2 is common in both terms. Factor 2 out of the expression. This can be written as: \[ 2(a + b) \]

Check by multiplying

To ensure the factorization is correct, multiply the factored expression back out. Multiply 2 by each term inside the parentheses: \[ 2(a + b) = 2a + 2b \] The original expression is regained, confirming that the factorization is correct.

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

Factoring is an essential concept in algebra. It involves breaking down an expression into a product of simpler expressions. Think of it as the reverse process of expanding. Just like multiplying is putting things together, factoring is breaking things apart. In our example, we started with the expression $2a + 2b$. By factoring, we aimed to express it as a product of two quantities. The first step was finding a common factor, which led us to factor out 2 and rewrite the expression as $2(a + b)$. This transforms a potentially complex equation into a simpler one, making it easier to solve or analyze.

common factors

A common factor is a number or variable that divides exactly into two or more terms. Finding common factors helps in the process of factoring. For instance, in the expression $2a + 2b$, the number 2 is a common factor. Both terms, 2a and 2b, share this factor. Once we identify the common factor, we can factor it out. This means we rewrite the expression as a product of this common factor and another simpler expression. Factoring out the common factor is like simplifying to make the expression easier to work with. For the example $2a + 2b$, factoring out 2 gives us $2(a + b)$.

algebraic expressions

Algebraic expressions are combinations of variables, numbers, and operations. Variables can be letters like 'a' or 'b', and the operations can include addition, subtraction, multiplication, and division. In the expression $2a + 2b$, we have two terms meant to be added together. Each term consists of a coefficient and a variable (2a and 2b). By factoring, we simplify the expression to $2(a + b)$. This makes the expression easier to understand and manipulate. It鈥檚 important to practice working with algebraic expressions, as they form the foundation of much of algebra and higher mathematics.

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Use the distributive law to factor each of the following. Check by multiplying. $$ 2 a+2 b $$

Short Answer

Step by step solution

Identify the common factor

Factor out the common factor

Check by multiplying

Key Concepts

factoring

common factors

algebraic expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.