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
![### Simplifying Algebraic Expressions
**Problem:**
Simplify the expression \(4x^{\frac{4}{3}} + 3x^{\frac{1}{3}}(2x + 4)\) by factoring out \(x^{\frac{1}{3}}\).
**Solution Steps:**
1. **Expression:**
\[
4x^{\frac{4}{3}} + 3x^{\frac{1}{3}}(2x + 4)
\]
2. **Factoring Approach:**
- We start by identifying the common factor of the terms in the expression, which is \(x^{\frac{1}{3}}\).
3. **Simplification:**
- Factor out \(x^{\frac{1}{3}}\) from both terms:
\[
x^{\frac{1}{3}}\left(4x^{\frac{4}{3}-\frac{1}{3}} + 3(2x + 4)\right)
\]
- This results in:
\[
x^{\frac{1}{3}}(4x + 6x + 12)
\]
4. **Combine Like Terms:**
- Simplify within the parentheses:
\[
x^{\frac{1}{3}}(10x + 12)
\]
5. **Final Simplified Expression:**
\[
x^{\frac{1}{3}}(10x + 12)
\]
By factoring out \(x^{\frac{1}{3}}\), we have successfully simplified the algebraic expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b4c38d1-e61f-4ae3-a015-72518f1ff016%2F45c0b2bd-4d7e-4a51-ac52-6d6e60259d8f%2Fwxcyd64_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Simplifying Algebraic Expressions
**Problem:**
Simplify the expression \(4x^{\frac{4}{3}} + 3x^{\frac{1}{3}}(2x + 4)\) by factoring out \(x^{\frac{1}{3}}\).
**Solution Steps:**
1. **Expression:**
\[
4x^{\frac{4}{3}} + 3x^{\frac{1}{3}}(2x + 4)
\]
2. **Factoring Approach:**
- We start by identifying the common factor of the terms in the expression, which is \(x^{\frac{1}{3}}\).
3. **Simplification:**
- Factor out \(x^{\frac{1}{3}}\) from both terms:
\[
x^{\frac{1}{3}}\left(4x^{\frac{4}{3}-\frac{1}{3}} + 3(2x + 4)\right)
\]
- This results in:
\[
x^{\frac{1}{3}}(4x + 6x + 12)
\]
4. **Combine Like Terms:**
- Simplify within the parentheses:
\[
x^{\frac{1}{3}}(10x + 12)
\]
5. **Final Simplified Expression:**
\[
x^{\frac{1}{3}}(10x + 12)
\]
By factoring out \(x^{\frac{1}{3}}\), we have successfully simplified the algebraic expression.
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