/*! 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 103 Perform each indicated operation... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 103

Perform each indicated operation. $$ 9 y^{2}-8 y^{2} $$

Short Answer

Expert verified
The result is \(y^2\).

Step by step solution

01

Identify Like Terms

Identify the terms in the expression. We have two terms: \(9y^2\) and \(-8y^2\). Both terms are "like terms" because they have the same variable part, which is \(y^2\).
02

Combine Like Terms

Combine the coefficients (numbers in front of the variable part) of the like terms. We do this by performing the indicated subtraction: \(9y^2 - 8y^2\).
03

Perform the Calculation

Subtract the coefficient of the second term from the coefficient of the first term: \(9 - 8 = 1\). So, the result of combining the like terms is \(1y^2\), which simplifies to \(y^2\).

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 the world of polynomial operations, identifying "like terms" is essential. Like terms are terms that have the same "variable part" raised to the same power. This means that in an expression, terms must not only match the variable but also its exponent to be considered like terms.
For instance, in the given problem, we have two terms: \(9y^2\) and \(-8y^2\). Both these terms are "like terms" because they share the same variable part, \(y^2\).
By recognizing like terms, you make it possible to combine them, simplifying the expression more easily.
Variable Parts
The "variable part" of a term is a crucial component to understand when performing polynomial operations. It determines whether terms can be combined. The variable part consists of the letter and its associated exponent.
In our example, the variable part is \(y^2\). It indicates that our variable is \(y\) and that it is squared. Knowing the correct variable part is essential because only terms with identical variable parts can be combined directly.
Always check that both the variable and its exponent match when identifying terms to combine.
Coefficients
In polynomials, these numbers directly influence how terms can be simplified or combined. Coefficients are the numbers in front of the variable part, such as the 9 in \(9y^2\) or the -8 in \(-8y^2\).
To combine like terms, you focus on their coefficients. You simply need to add or subtract the coefficients, depending on the operation specified. In our case, subtracting the coefficient of \(-8y^2\) from \(9y^2\) results in \(1y^2\).
Therefore, mastering how to add and subtract coefficients greatly aids in simplifying polynomial expressions.
Subtraction
Subtracting terms in polynomials can initially seem tricky, but it's easier when you focus on the coefficients. Subtraction in polynomial expressions involves taking the coefficient of one term away from the coefficient of another.
For the like terms \(9y^2\) and \(-8y^2\), the subtraction is straightforward. You subtract 8 from 9, resulting in \(1\). It's important to follow through this calculation to ensure accuracy, which in our case simplifies the expression to \(y^2\).
Properly executing subtraction between coefficients is key to arriving at the correct simplified polynomial expression.

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

Solve. $$ x+\sqrt{x+5}=7 $$

Determine the smallest number both the numerator and denominator should be multiplied by to rationalize the denominator of the radical expression. \(\frac{5}{\sqrt{27}}\)

Solve. $$ \sqrt[3]{6 x-3}-3=0 $$

Consider the equations \(\sqrt{2 x}=4\) and \(\sqrt[3]{2 x}=4\) a. Explain the difference in solving these equations. b. Explain the similarity in solving these equations.

Solve. $$ \sqrt[3]{-6 x-1}=\sqrt[3]{-2 x-5} $$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.