Problem 104 Simplify. $$ 8 n^{2}-3 n+2\l... [FREE SOLUTION]

Chapter 1: Problem 104

Simplify. $$ 8 n^{2}-3 n+2\left(n-4 n^{2}\right) $$

Short Answer

Expert verified

$-n$

Step by step solution

Combine Like Terms

Identify and combine like terms within the expression. The given expression is dependent on one variable, so group the terms accordingly.

Distribute and Simplify

Distribute the 2 in the term $2(n - 4n^{2})$ to get $2n - 8n^{2}$. Now rewrite the expression: $8n^{2} - 3n + 2n - 8n^{2}$.

Combine Similar Terms Again

Combine the terms with $n^{2}$ and the linear terms. $8n^{2} - 8n^{2} + (-3n + 2n)$ simplifies to $0 + (-n)$ which is $-n$.

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.

Combining Like Terms

When simplifying algebraic expressions, it's crucial to combine like terms. Like terms are terms that have the same variables raised to the same power. For example, in the expression provided, both the terms containing $n^{2}$ and those containing $n$ can be combined separately. This process involves adding or subtracting the coefficients of these like terms. Combining like terms helps us condense the expression, making it easier to work with and understand. In our example, we started by identifying and grouping all terms involving $n^{2}$ and all linear terms involving just $n$.

Distribution

The next step is distribution. This means multiplying each term inside the parentheses by the number outside. In our exercise, we distribute the 2 across the terms inside the parentheses $2(n - 4n^{2})$. That gives us $2 \times n - 2 \times 4n^{2} = 2n - 8n^{2}$. Distribution helps to eliminate parentheses and results in a simpler expression. Once distributed, the expression becomes easier to combine further. In this step, the expression $8n^{2} - 3n + 2(n - 4n^{2})$ becomes $8n^{2} - 3n + 2n - 8n^{2}$.

Linear Terms

Linear terms are the terms with the variable raised to the power of one, such as $n$ in our exercise. These terms, when combined, simplify the expression further. For instance, in the final step, we combined the linear terms $-3n$ and $2n$ to get $-n$. Recognizing and combining linear terms is essential because it helps in simplifying the expression entirely. After combining the like terms and distributing, our expression reduced to $-n$. This simplification process is a tidy and systematic method to arrive at the most simplified form of an algebraic expression.

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

Simplify. $$ 8 n^{2}-3 n+2\left(n-4 n^{2}\right) $$

Short Answer

Step by step solution

Combine Like Terms

Distribute and Simplify

Combine Similar Terms Again

Key Concepts

Combining Like Terms

Distribution

Linear Terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Logic and Functions

Applied Mathematics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.