Problem 101 Simplify. $$ 3 x^{2}+7-\left... [FREE SOLUTION]

Chapter 1: Problem 101

Simplify. $$ 3 x^{2}+7-\left(2 x^{2}+5\right) $$

Short Answer

Expert verified

x^2 + 2

Step by step solution

Distribute the Negative Sign

First, distribute the negative sign to each term inside the parentheses. This changes the expression to: 3x^2 + 7 - 2x^2 - 5

Combine Like Terms

Next, combine the like terms. The like terms are the ones with the variable $x^2$ and the constant terms: $3x^2 - 2x^2$ and $7 - 5$

Simplify

Simplify the expression by performing the arithmetic. $3x^2 - 2x^2= x^2$ and $7-5 = 2$. So the simplified expression is: $x^2 + 2$

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.

distributive property

To start simplifying the algebraic expression, we need to use the distributive property to manage the negative sign. This is crucial before combining any terms. When you have an expression like \ - (2x^2 + 5)\, the negative sign in front of the parentheses signifies that each term inside must be multiplied by -1.
Thus, distributing the negative sign inside the expression changes it into: \[ 3x^2 + 7 - 2x^2 - 5 \]
This transformation helps to eliminate the parentheses and sets up the expression perfectly for the next step.

combining like terms

Once you have distributed the negative sign and removed the parentheses, the next step is to identify and combine like terms in the expression. Like terms are terms that have the same variable raised to the same power.
In our case, we look for terms that include $x^2$, which are $3x^2$ and $-2x^2$.
We also identify the constant terms, which are $7$ and $-5$.
By combining these like terms, we get:
\[ 3x^2 - 2x^2 \] and \[ 7 - 5 \]
This combination simplifies the expression further.

simplifying algebraic expressions

The final step involves performing the arithmetic needed to simplify the expression completely. We've already combined our like terms:
\[ 3x^2 - 2x^2 \] simplifies to \ x^2\
and \[ 7 - 5 \] simplifies to \ 2 \
So putting it all together, our simplified expression is \ x^2 + 2 \
Remember, the goal of simplifying algebraic expressions is to make them as simple as possible, but they should also remain equivalent to the original expression. By following these steps, you ensure clarity and accuracy in your solutions.

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. $$ 3 x^{2}+7-\left(2 x^{2}+5\right) $$

Short Answer

Step by step solution

Distribute the Negative Sign

Combine Like Terms

Simplify

Key Concepts

distributive property

combining like terms

simplifying algebraic expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Logic and Functions

Probability and Statistics

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.