Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Problem c: Simplification of an Algebraic Expression
**Given:**
\[ y = (3x + 5)(x^2 - 4) \]
**Objective:**
Simplify the expression.
**Steps to Simplify:**
1. **Distribute each term in the first bracket by each term in the second bracket:**
\[
y = (3x \cdot x^2) + (3x \cdot -4) + (5 \cdot x^2) + (5 \cdot -4)
\]
2. **Calculate each multiplication:**
\[
y = 3x^3 - 12x + 5x^2 - 20
\]
3. **Rearrange the terms in descending order of their exponents:**
\[
y = 3x^3 + 5x^2 - 12x - 20
\]
**Result:**
The simplified expression is:
\[ y = 3x^3 + 5x^2 - 12x - 20 \]
---
This solution involves distributing the terms and arranging them in order of decreasing exponents, which is a common method in algebra to simplify expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3360c4a6-c639-41c4-ba15-42ca4b2b8c54%2F88430b93-4059-4c9b-821a-cc0914da8bdc%2Fx7d0jm_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem c: Simplification of an Algebraic Expression
**Given:**
\[ y = (3x + 5)(x^2 - 4) \]
**Objective:**
Simplify the expression.
**Steps to Simplify:**
1. **Distribute each term in the first bracket by each term in the second bracket:**
\[
y = (3x \cdot x^2) + (3x \cdot -4) + (5 \cdot x^2) + (5 \cdot -4)
\]
2. **Calculate each multiplication:**
\[
y = 3x^3 - 12x + 5x^2 - 20
\]
3. **Rearrange the terms in descending order of their exponents:**
\[
y = 3x^3 + 5x^2 - 12x - 20
\]
**Result:**
The simplified expression is:
\[ y = 3x^3 + 5x^2 - 12x - 20 \]
---
This solution involves distributing the terms and arranging them in order of decreasing exponents, which is a common method in algebra to simplify expressions.
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