/*! 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 160 Find an equivalent expression by... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 160

Find an equivalent expression by factoring. $$ a b+b $$

Short Answer

Expert verified
The factored expression is \(b(a + 1)\).

Step by step solution

01

Identify the Common Factor

Examine the given expression to identify terms that have a common factor. In the expression \(ab + b\), both terms share the common factor \(b\).
02

Factor Out the Common Factor

Extract the common factor \(b\) from both terms. This can be done by factoring \(b\) out of each term:\[ab + b = b(a + 1)\]
03

Write the Factored Expression

After factoring out the common factor, write the expression in its factored form. The equivalent expression is \(b(a + 1)\).

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.

Common Factor
When dealing with algebraic expressions, it's important to identify common factors. A common factor is a number or a variable that divides each term in an expression. Seeing common factors can simplify expressions and solve problems more easily.

Let's revisit our expression: a b + b . Here, both terms include the variable 'b'. This means 'b' is a common factor of both terms. Recognizing this common factor is the first step in the process of factoring. Once you spot the common factor, you are on your way to simplifying the expression.
Factoring Techniques
After identifying the common factor in an expression, the next step is to use factoring techniques to simplify it. Factoring techniques involve extracting the common factor from each term.

For the expression: ab + b , we identified 'b' as the common factor. We then factor 'b' out of each term: [ab + b = b(a + 1)] .

Notice how we take 'b' outside of the parentheses and are left with (a + 1) inside. This technique can be applied to more complex expressions as well, breaking them down into simpler terms.
Equivalent Expressions
By factoring an expression, we find an equivalent expression that might be easier to work with. Equivalent expressions are different forms of the same expression. They have the same value but may look different due to transformations like factoring or expanding.

In our example, the original expression a b + b is equivalent to the factored form b(a + 1). Both expressions are equal, meaning they will yield the same result for any value of 'a' and 'b'.

Understanding equivalent expressions is crucial, as it allows flexibility in solving equations and simplifying algebraic problems.

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

Which numbers in the list provided are (a) whole numbers? (b) integers? (c) rational numbers? (d) irrational numbers? (e) real numbers?. $$ -6.08,-5,0,1, \sqrt{17}, \frac{99}{2} $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ |-2-3| \cdot 4^{2}-3 $$

Write an equivalent expression using an associative law. $$ -7(a b) $$

Use set-builder notation to write each set. \(\\{24,26,28,30,32\\}\)

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ 196 \in \mathbb{N} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.