Problem 44 Combine like terms. $$ 4 x^{... [FREE SOLUTION]

Chapter 5: Problem 44

Combine like terms. $$ 4 x^{2}+2 x-6 x^{2}-6 $$

Short Answer

Expert verified

-2x^{2} + 2x - 6

Step by step solution

Identify like terms involving $x^2$

Look at the terms: $4x^{2}$ and $-6x^{2}$. These are like terms because they both have the same variable raised to the same power.

Combine $x^2$ terms

Combine the coefficients of the $x^2$ terms: $4x^{2} - 6x^{2} = -2x^{2}$.

Identify the remaining terms

The remaining terms are $2x$ and $-6$. These are not like terms with any other term in the expression.

Write the simplified expression

Combine all the terms together: $-2x^{2} + 2x - 6$.

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.

Polynomials

Polynomials are mathematical expressions consisting of variables, operations (like addition or multiplication), and coefficients (which we'll talk about next). An example of a polynomial is this expression: $4x^2 + 2x - 6x^2 - 6$. This polynomial includes terms with variables raised to different powers, such as $x^2$ and $x$. Polynomials can be simple, with just one term, or complex, with many variable terms combined through addition or subtraction. The degree of the polynomial is given by the highest power of the variable in the expression. In our exercise, the highest degree term is $x^2$, making the polynomial a second-degree polynomial.

Coefficients

Coefficients are the numerical parts of the terms in a polynomial. In the expression $4x^2 + 2x - 6x^2 - 6$, the numbers 4, 2, -6, and -6 are all coefficients. These numbers indicate how many times a term should be counted. For example, in $4x^2$, 4 is the coefficient telling us we have four $x^2$ terms. Similarly, in $-6x^2$, -6 tells us we have six $-x^2$ terms. Identifying and working with coefficients is crucial when combining like terms in polynomials. To combine terms, add or subtract their coefficients while keeping the same variable part.

Simplifying Expressions

Simplifying expressions involves combining like terms to make the expression easier to work with. Like terms are terms that have the same variables raised to the same power. In our example, $4x^2$ and $-6x^2$ are like terms because they both involve $x^2$. We can combine these by adding their coefficients: $4 - 6 = -2$. The simplified form of their combination is $-2x^2$.
For terms that don't have the same variables or powers, like $2x$ and $-6$ in our example, we simply bring them down as they are. The final simplified expression from our example will hence be $-2x^2 + 2x - 6$. This process makes polynomial expressions much easier to handle and understand.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Combine like terms. $$ 4 x^{2}+2 x-6 x^{2}-6 $$

Short Answer

Step by step solution

Identify like terms involving \(x^2\)

Combine \(x^2\) terms

Identify the remaining terms

Write the simplified expression

Key Concepts

Polynomials

Coefficients

Simplifying Expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Probability and Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.