/*! 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 49 Subtract \(\left(7 w^{2}-4 w+2\r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 49

Subtract \(\left(7 w^{2}-4 w+2\right)\) from \(\left(8 w^{2}-w+6\right)\).

Short Answer

Expert verified
w^{2} + 3w + 4

Step by step solution

01

Understand the Problem

We are given two quadratic expressions and asked to subtract the first one from the second one. The expressions are \((7w^{2} - 4w + 2)\) and \((8w^{2} - w + 6)\).
02

Write Down the Subtraction

We need to subtract the first expression from the second: \((8w^{2} - w + 6) - (7w^{2} - 4w + 2)\).
03

Distribute the Negative Sign

Distribute the negative sign to each term in the second expression: \(8w^{2} - w + 6 - 7w^{2} + 4w - 2\).
04

Combine Like Terms

Combine the like terms: \(8w^{2} - 7w^{2}\), \(-w + 4w\) and \(6 - 2\). This gives us \(w^{2} + 3w + 4\).

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.

Quadratic Expressions
A quadratic expression is a polynomial of degree 2. This means that the highest power of the variable (in this case, 'w') is 2.
Quadratic expressions have the general form: a w^2 + b w + c where a, b , and c are constants (numbers).
For example, in the expression 8 w^2 - w + 6, the coefficient of w^2 is 8, the coefficient of w is -1, and the constant term is 6.
When working with quadratic expressions, it鈥檚 important to focus on the coefficients and constant terms.
This makes it easier when you need to perform operations like addition, subtraction, and factoring.
Distributing Negative Sign
When you perform algebraic subtraction, particularly with polynomials, distributing the negative sign is a crucial step.
It ensures that all terms in the expression being subtracted are correctly negated.
In the problem (8 w^2 - w + 6) - (7 w^2 - 4 w + 2), distributing the negative sign means you make each term in (7 w^2 - 4 w + 2) its opposite.Here鈥檚 how it looks:
    (8 w^2 - w + 6) - (7 w^2 - 4 w + 2) becomes 8 w^2 - w + 6 - 7 w^2 + 4w - 2.
    We change + 7 w^2 todistribute7 w^2, - 4 w to + 4 w, and + 2 to - 2.
This step is fundamental because incorrect distribution can lead to errors in your final expression.
Always double-check that each term has been properly negated.
Combining Like Terms
After distributing the negative sign, the next step in algebraic subtraction is to combine like terms.
Like terms are terms that have the same variable raised to the same power.
    For instance, in the expression 8 w^2 - 7 w^2 + 4 w - w + 6 - 2, we have the following like terms to combine:
    8 w^2 and -7 w^2 are like terms because they both contain the variable w raised to the power of 2.
    -w and 4 w are like terms because they both have the variable w (no exponent). 6 and -2 are like terms because they are constant terms (they don't have the variable w). Combining these like terms gives us: 1) 8 w^2 - 7 w^2 = w^2 2) -w + 4 w = 3 w 3) 6 - 2 = 4 Putting it all together, we get the simplified expression: w^2 + 3 w + 4.
    This method of combining like terms makes complex expressions more manageable and simplifies the solution process.

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

Divide \(\frac{10 x^{2}+x-12}{2 x}\) and explain with words how you get each term of the quotient.

Divide each polynomial by the monomial. $$\frac{20 b^{2}-12 b}{-4}$$

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

Divide the monomials. $$\frac{18 a^{4} b^{8}}{-27 a^{9} b^{5}}$$

Divide the monomials. $$\frac{45 x^{5} y^{9}}{-60 x^{8} y^{6}}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Pure 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.