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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![### Steps to Solve and Explain Polynomial Expression Problem
#### Step 2: Solve the Problem
Show any and all work.
#### Step 3: Type Explanation of Answers
---
### Problem Statement:
**Find the polynomial expression equivalent to \( (3p + 2)^2 \).**
### Solution:
To solve this problem, we need to expand the expression \( (3p + 2)^2 \). Here’s a detailed step-by-step process:
1. **Apply the Binomial Theorem:**
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
In this case, \( a = 3p \) and \( b = 2 \).
2. **Substitute the values into the formula:**
\[ (3p + 2)^2 = (3p)^2 + 2 \cdot (3p) \cdot 2 + 2^2 \]
3. **Calculate each term separately:**
- Calculate \( (3p)^2 \):
\[ (3p)^2 = 9p^2 \]
- Calculate \( 2 \cdot (3p) \cdot 2 \):
\[ 2 \cdot (3p) \cdot 2 = 2 \cdot 3p \cdot 2 = 12p \]
- Calculate \( 2^2 \):
\[ 2^2 = 4 \]
4. **Combine all terms:**
\[ (3p + 2)^2 = 9p^2 + 12p + 4 \]
Thus, the polynomial expression equivalent to \( (3p + 2)^2 \) is \[ 9p^2 + 12p + 4 \].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65f9c7e9-67e0-4976-9b1c-b8c494c4cb48%2F9c586d53-9ca5-4275-b8ba-bfd7cc7106a5%2F7ox090k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Steps to Solve and Explain Polynomial Expression Problem
#### Step 2: Solve the Problem
Show any and all work.
#### Step 3: Type Explanation of Answers
---
### Problem Statement:
**Find the polynomial expression equivalent to \( (3p + 2)^2 \).**
### Solution:
To solve this problem, we need to expand the expression \( (3p + 2)^2 \). Here’s a detailed step-by-step process:
1. **Apply the Binomial Theorem:**
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
In this case, \( a = 3p \) and \( b = 2 \).
2. **Substitute the values into the formula:**
\[ (3p + 2)^2 = (3p)^2 + 2 \cdot (3p) \cdot 2 + 2^2 \]
3. **Calculate each term separately:**
- Calculate \( (3p)^2 \):
\[ (3p)^2 = 9p^2 \]
- Calculate \( 2 \cdot (3p) \cdot 2 \):
\[ 2 \cdot (3p) \cdot 2 = 2 \cdot 3p \cdot 2 = 12p \]
- Calculate \( 2^2 \):
\[ 2^2 = 4 \]
4. **Combine all terms:**
\[ (3p + 2)^2 = 9p^2 + 12p + 4 \]
Thus, the polynomial expression equivalent to \( (3p + 2)^2 \) is \[ 9p^2 + 12p + 4 \].
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