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,...
Related questions
Question
![**Example Problem for Students:**
### Problem:
**Multiply and simplify the expression:**
\[
(x - 2y)(x + 2y)
\]
### Select one of the following options:
- A. \(x^2 + 2y^2\)
- B. \(x^2 + 4y^2\)
- C. \(x^2 - 4xy - 4y^2\)
- D. \(x^2 - 4y^2\)
### Solution Explanation:
Utilize the difference of squares formula \((a - b)(a + b) = a^2 - b^2\) to simplify the given expression:
\[
(x - 2y)(x + 2y) = x^2 - (2y)^2 = x^2 - 4y^2
\]
Thus, the correct answer is:
- **D. \(x^2 - 4y^2\)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e3b61c9-20cc-45b0-8820-712e68e1a019%2Fdc73beb7-f162-4d5b-ae7f-ec7968816671%2Fa82emsl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example Problem for Students:**
### Problem:
**Multiply and simplify the expression:**
\[
(x - 2y)(x + 2y)
\]
### Select one of the following options:
- A. \(x^2 + 2y^2\)
- B. \(x^2 + 4y^2\)
- C. \(x^2 - 4xy - 4y^2\)
- D. \(x^2 - 4y^2\)
### Solution Explanation:
Utilize the difference of squares formula \((a - b)(a + b) = a^2 - b^2\) to simplify the given expression:
\[
(x - 2y)(x + 2y) = x^2 - (2y)^2 = x^2 - 4y^2
\]
Thus, the correct answer is:
- **D. \(x^2 - 4y^2\)**
![### Mathematics Problem: Polynomial Multiplication
#### Problem Statement
Multiply and simplify:
\[
(x^3 - y^2)(x^3 + y^2)
\]
#### Options
Select one:
A. \(x^9 - y^4\)
B. \(x^6 - y^4\)
C. \(x^9 + y^4\)
D. \(x^6 + y^4\)
---
This problem requires you to use the distributive property (also known as the FOIL method for binomials) to multiply the given polynomials and then simplify the result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e3b61c9-20cc-45b0-8820-712e68e1a019%2Fdc73beb7-f162-4d5b-ae7f-ec7968816671%2Ftexrk6g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Mathematics Problem: Polynomial Multiplication
#### Problem Statement
Multiply and simplify:
\[
(x^3 - y^2)(x^3 + y^2)
\]
#### Options
Select one:
A. \(x^9 - y^4\)
B. \(x^6 - y^4\)
C. \(x^9 + y^4\)
D. \(x^6 + y^4\)
---
This problem requires you to use the distributive property (also known as the FOIL method for binomials) to multiply the given polynomials and then simplify the result.
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