/*! 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 25 Add or subtract the monomials. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 25

Add or subtract the monomials. $$a^{2} b-4 a-5 a b^{2}$$

Short Answer

Expert verified
\(a^{2} b - 4a - 5a b^{2}\)

Step by step solution

01

Identify the Monomials

The given expression consists of three terms: \(a^{2} b\), \(-4a\), and \(-5a b^{2}\). Each of these terms is a monomial.
02

Check for Like Terms

Like terms in algebra are terms that contain the same variables raised to the same power. Here, none of the terms contain the same combination of variables and exponents: \(a^{2} b\), \(a\), and \(a b^{2}\) are all different.
03

Combine the Terms

Since there are no like terms to combine, the expression remains as is: \(a^{2} b - 4a - 5a b^{2}\).

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 algebra, 'like terms' are terms that have the exact same variable factors raised to the same power. This makes them compatible for addition or subtraction.
For example:
  • The terms \(3a^{2}b\) and \(7a^{2}b\) are 'like terms' because they both have \(a^{2}b\) as their variables raised to the same powers.
  • However, \(a^{2}b\) and \(ab^{2}\) are not 'like terms' because the exponents of the variables differ.
  • Similarly, \(4x\) and \(4x^{3}\) are also not 'like terms' for the same reason.

Identifying 'like terms' helps us simplify complex expressions.
When adding or subtracting expressions:
  • Combine only 'like terms' by adding or subtracting their coefficients.
  • If there are no 'like terms', the expression remains as it is.
Understanding 'like terms' makes it easier to manage and solve equations.
algebraic expressions
'Algebraic expressions' are mathematical phrases that can contain numbers, variables, and operation symbols (such as +, -, *, /).
They do not include an equal sign, unlike algebraic equations.
For example, \(3a^{2}b + 7a - 5\) is an algebraic expression.
The key components of algebraic expressions are:
  • Terms 鈥� The parts of the expression separated by + or - signs. Each term can be a constant, a variable, or a product of constants and variables. Like in our example: \(a^{2}b, \ -4a, \ and\ -5ab^{2}\)
  • Coefficients 鈥擳he numerical part of the terms. Like \(-4\), \(-5\)
  • Variables 鈥� The letters used to represent numbers. For instance, a, b in our case.
The main goal when working with algebraic expressions is to simplify or rearrange them to facilitate easier calculations or problem solving.
monomials
A 'monomial' is a type of algebraic expression that has only one term. It responds to the product, typically, of constants and variables.
For example, \(5x^{3}y\), \(7a\), and \(12b^{2}c\) are all monomials.
The essential characteristics of monomials include:
  • Single term 鈥� Unlike an algebraic expression, a monomial does not have addition or subtraction signs connecting multiple terms.
  • Product of constants and variables 鈥� Monomials are formed by multiplying constants (numbers) and variables (letters).
Monomials play a crucial role in polynomial expressions and are fundamental components in algebra. When working with monomials:
  • Identify and combine 'like terms' in more complex expressions.
  • Recognize that each monomial term can only be added or subtracted with another identical variable and exponent term.
Understanding what monomials are helps simplify many algebra 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

Determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial. (a) \(8-3 x\) (b) \(z^{2}-5 z-6\) (c) \(y^{3}-8 y^{2}+2 y-16\) (d) \(81 b^{5}-24 b^{3}+1\) (e) -18

One megabyte is approximately \(10^{6}\) bytes. One gigabyte is approximately \(10^{9}\) bytes. How many megabytes are in one gigabyte?

Determine the degree of each polynomial. (a) \(14-29 x\) (b) \(z^{2}-5 z-6\) (c) \(y^{3}-8 y^{2}+2 y-16\) (d)\(23 a b^{2}-14\) (e) -3

Simplify. (a) \(3 \cdot 5^{-1}\) (b) \((3 \cdot 5)^{-1}\)

Multiply. $$(w-6) \cdot 8$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.