/*! 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 42 Simplify. $$20 b-15 b$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 42

Simplify. $$20 b-15 b$$

Short Answer

Expert verified
The simplified form of the given expression is \(5b\).

Step by step solution

01

Identify Like Terms

In algebra, terms that have the same variable part are called 'like terms'. Here, both \(20b\) and \(-15b\) are like terms as they contain the same variable \(b\).
02

Apply Subtraction Rule

The subtraction rule in algebra allows us to combine like terms. Simply subtract the numerical coefficient of the second term from the first term. \(20b - 15b = 5b\)

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.

Like Terms
In the world of algebra, identifying like terms is a fundamental skill that helps in simplifying expressions. Like terms have identical variable parts. For instance, when you see terms like \(20b\) and \(-15b\), both of these terms are considered 'like' because they share the common variable \(b\).

This means that, regardless of the numbers multiplying them (called coefficients), they can be combined together. When simplifying expressions, always start by spotting and grouping these like terms. This makes algebraic manipulation much easier!
Subtraction Rule
The subtraction rule in algebra is essential for combining like terms efficiently. Suppose you have two like terms, for example, \(20b\) and \(-15b\).

To apply the subtraction rule, you perform simple arithmetic on the coefficients of these terms (these are the numbers before the variable). So, you subtract the coefficient of the second term from the first:
  • First term's coefficient: 20
  • Second term's coefficient: -15 (note the subtraction sign)
Carrying out the subtraction, you have \(20 - 15 = 5\), thus simplifying the expression to \(5b\).

This rule helps streamline expressions by making them less complex and more manageable. Understanding and applying the subtraction rule is crucial.
Algebraic Coefficients
Coefficients play a crucial role in algebraic expressions. They are the numbers that multiply variables, giving value to each term. For example, in the terms \(20b\) and \(-15b\), the coefficients are 20 and -15, respectively.

When working with coefficients, one must observe the arithmetic operations dictated by the expression. In simplification, these coefficients are either added or subtracted based on the rule being applied.

Getting comfortable with identifying and manipulating coefficients can greatly help in making sense of algebraic expressions.
  • Positive and negative signs of coefficients must be considered during operations.
  • Coefficients determine the numeric value of a term.
  • Simplifying expressions becomes smoother with a good grasp of coefficients.
By understanding coefficients, you lay a strong foundation for mastering 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

The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance. For one driver, the stopping distance \(d\) is given by the function \(d=f(v)=0.04 v^{2}+0.9 v,\) where \(v\) is the velocity of the car. Find the stopping distance when the driver is traveling at \(30 \mathrm{mph}\).

Perform the operation. Subtract \((2 x+5 y)\) from \((5 x-8 y)\)

$$\text { If } x=105, \text { evaluate } \frac{x^{500}-x^{499}}{x^{499}}$$

Simplify or solve as appropriate. $$(2 s-3)(s+2)=(2 s+1)(s-3)$$

Perform the operations. $$-\left(-3 z^{2}-4 z+7\right)+\left(2 z^{2}+2 z-1\right)-\left(2 z^{2}-3 z+7\right)$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics 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.