Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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![**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-](https://content.bartleby.com/qna-images/question/dd091649-5055-4a22-b0f4-f6b331627703/d52f6122-2e18-4a2c-99de-46331bb0c624/sb8d1gqs_processed.jpeg)
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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