Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![### Multiply and Simplify Polynomial Expressions
#### Problem Statement:
Multiply and simplify the following expression:
\[ -4x(3x^5 - 4x^2 + x) \]
#### Answer Choices:
Select one of the following:
- A. \(-12x^5 + 16x^3 - 4x^2\)
- B. \(-12x^6 + 16x^3 - 4x^2\)
- C. \(-12x^5 - 16x^3 + 4x^2\)
- D. \(12x^6 + 16x^3 - 4x^2\)
- E. \(-12x^6 - 16x^3 - 4x^2\)
### Solution Process:
To simplify the expression \( -4x(3x^5 - 4x^2 + x) \), distribute \(-4x\) to each term inside the parentheses:
1. \(-4x \cdot 3x^5 = -12x^{5+1} = -12x^6\)
2. \(-4x \cdot (-4x^2) = 16x^{2+1} = 16x^3\)
3. \(-4x \cdot x = -4x^{1+1} = -4x^2\)
The simplified expression is:
\[
-12x^6 + 16x^3 - 4x^2
\]
#### Correct Answer:
- **B. \(-12x^6 + 16x^3 - 4x^2\)**
This simplifies the original expression correctly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e3b61c9-20cc-45b0-8820-712e68e1a019%2Ff27fcc4c-927a-41af-971e-467a932ab81e%2Fq0oh5hk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Multiply and Simplify Polynomial Expressions
#### Problem Statement:
Multiply and simplify the following expression:
\[ -4x(3x^5 - 4x^2 + x) \]
#### Answer Choices:
Select one of the following:
- A. \(-12x^5 + 16x^3 - 4x^2\)
- B. \(-12x^6 + 16x^3 - 4x^2\)
- C. \(-12x^5 - 16x^3 + 4x^2\)
- D. \(12x^6 + 16x^3 - 4x^2\)
- E. \(-12x^6 - 16x^3 - 4x^2\)
### Solution Process:
To simplify the expression \( -4x(3x^5 - 4x^2 + x) \), distribute \(-4x\) to each term inside the parentheses:
1. \(-4x \cdot 3x^5 = -12x^{5+1} = -12x^6\)
2. \(-4x \cdot (-4x^2) = 16x^{2+1} = 16x^3\)
3. \(-4x \cdot x = -4x^{1+1} = -4x^2\)
The simplified expression is:
\[
-12x^6 + 16x^3 - 4x^2
\]
#### Correct Answer:
- **B. \(-12x^6 + 16x^3 - 4x^2\)**
This simplifies the original expression correctly.
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