Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Simplifying Expressions - Practice Problem**
**Mathematical Practice Problem:**
**Simplify** \( (3a^2 + 1) - (4 + 2a^2) \). Write the answer in standard form.
**Instructions:**
1. Carefully examine the expression inside the parentheses.
2. Apply the distributive property where necessary.
3. Combine like terms.
**Standard Form:**
In general, the standard form for expressing a polynomial is to arrange the terms in descending order of their exponents.
**Example:**
Given the problem \( (3a^2 + 1) - (4 + 2a^2) \), follow these steps:
1. Distribute the negative sign to both terms inside the second set of parentheses:
\[
(3a^2 + 1) - 4 - 2a^2
\]
2. Combine like terms:
\[
3a^2 - 2a^2 + 1 - 4
\]
3. Simplify the expression:
\[
3a^2 - 2a^2 = a^2
\]
\[
1 - 4 = -3
\]
\[
\therefore \text{The simplified expression is: } a^2 - 3
\]
Enter your final answer in the provided text box.
**Note:** Ensure your answer follows the standard form, with the terms arranged based on the exponent of \( a \) in descending order.
Submit your answers to check for correctness and receive feedback.
-End of Practice Problem-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd091649-5055-4a22-b0f4-f6b331627703%2Fd52f6122-2e18-4a2c-99de-46331bb0c624%2Fsb8d1gqs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Simplifying Expressions - Practice Problem**
**Mathematical Practice Problem:**
**Simplify** \( (3a^2 + 1) - (4 + 2a^2) \). Write the answer in standard form.
**Instructions:**
1. Carefully examine the expression inside the parentheses.
2. Apply the distributive property where necessary.
3. Combine like terms.
**Standard Form:**
In general, the standard form for expressing a polynomial is to arrange the terms in descending order of their exponents.
**Example:**
Given the problem \( (3a^2 + 1) - (4 + 2a^2) \), follow these steps:
1. Distribute the negative sign to both terms inside the second set of parentheses:
\[
(3a^2 + 1) - 4 - 2a^2
\]
2. Combine like terms:
\[
3a^2 - 2a^2 + 1 - 4
\]
3. Simplify the expression:
\[
3a^2 - 2a^2 = a^2
\]
\[
1 - 4 = -3
\]
\[
\therefore \text{The simplified expression is: } a^2 - 3
\]
Enter your final answer in the provided text box.
**Note:** Ensure your answer follows the standard form, with the terms arranged based on the exponent of \( a \) in descending order.
Submit your answers to check for correctness and receive feedback.
-End of Practice Problem-
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