**Mathematics Problem Transcription** --- ### Problem 1: \[ 3x^2 \sqrt{x^2 - 36} + x^3 \cdot \frac{1}{2} (x^2 - 36)^{-1/2} \cdot 2x = \] ### Problem 2: \[ 3x^2 (x^2 - 36) + x^4 \] \[ \sqrt{x^2 - 36} \] --- **Detailed Description:** 1. **Problem 1:** This equation combines polynomial and radical expressions. It consists of a term with a square root, product of polynomials, and a product of fractional exponents: - The first term is \(3x^2 \sqrt{x^2 - 36}\). - The second term involves several components: \( x^3 \), the fraction \(\frac{1}{2}\), the radical \((x^2 - 36)^{-1/2}\) raised to a negative fractional exponent, and multiplied by \( 2x \). 2. **Problem 2:** This problem is an entirely different expression written methodically: - The numerator is composed of two terms: \( 3x^2 (x^2 - 36) \) and \( x^4 \). - The denominator is a square root: \( \sqrt{x^2 - 36} \). Given the algebraic complexity, these problems likely pertain to calculus or pre-calculus topics for high school or university-level coursework, focusing on polynomial and radical expressions.
**Mathematics Problem Transcription** --- ### Problem 1: \[ 3x^2 \sqrt{x^2 - 36} + x^3 \cdot \frac{1}{2} (x^2 - 36)^{-1/2} \cdot 2x = \] ### Problem 2: \[ 3x^2 (x^2 - 36) + x^4 \] \[ \sqrt{x^2 - 36} \] --- **Detailed Description:** 1. **Problem 1:** This equation combines polynomial and radical expressions. It consists of a term with a square root, product of polynomials, and a product of fractional exponents: - The first term is \(3x^2 \sqrt{x^2 - 36}\). - The second term involves several components: \( x^3 \), the fraction \(\frac{1}{2}\), the radical \((x^2 - 36)^{-1/2}\) raised to a negative fractional exponent, and multiplied by \( 2x \). 2. **Problem 2:** This problem is an entirely different expression written methodically: - The numerator is composed of two terms: \( 3x^2 (x^2 - 36) \) and \( x^4 \). - The denominator is a square root: \( \sqrt{x^2 - 36} \). Given the algebraic complexity, these problems likely pertain to calculus or pre-calculus topics for high school or university-level coursework, focusing on polynomial and radical expressions.
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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please explain the simplifaction from step one to step two.
![**Mathematics Problem Transcription**
---
### Problem 1:
\[ 3x^2 \sqrt{x^2 - 36} + x^3 \cdot \frac{1}{2} (x^2 - 36)^{-1/2} \cdot 2x = \]
### Problem 2:
\[ 3x^2 (x^2 - 36) + x^4 \]
\[ \sqrt{x^2 - 36} \]
---
**Detailed Description:**
1. **Problem 1:**
This equation combines polynomial and radical expressions. It consists of a term with a square root, product of polynomials, and a product of fractional exponents:
- The first term is \(3x^2 \sqrt{x^2 - 36}\).
- The second term involves several components: \( x^3 \), the fraction \(\frac{1}{2}\), the radical \((x^2 - 36)^{-1/2}\) raised to a negative fractional exponent, and multiplied by \( 2x \).
2. **Problem 2:**
This problem is an entirely different expression written methodically:
- The numerator is composed of two terms: \( 3x^2 (x^2 - 36) \) and \( x^4 \).
- The denominator is a square root: \( \sqrt{x^2 - 36} \).
Given the algebraic complexity, these problems likely pertain to calculus or pre-calculus topics for high school or university-level coursework, focusing on polynomial and radical expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa451162e-14ac-4cfd-a2c6-1eae7f4a5f1a%2Fc03b9a07-d8d1-4e5c-91c2-2d50d809af07%2Fddwgp4_processed.png&w=3840&q=75)
Transcribed Image Text:**Mathematics Problem Transcription**
---
### Problem 1:
\[ 3x^2 \sqrt{x^2 - 36} + x^3 \cdot \frac{1}{2} (x^2 - 36)^{-1/2} \cdot 2x = \]
### Problem 2:
\[ 3x^2 (x^2 - 36) + x^4 \]
\[ \sqrt{x^2 - 36} \]
---
**Detailed Description:**
1. **Problem 1:**
This equation combines polynomial and radical expressions. It consists of a term with a square root, product of polynomials, and a product of fractional exponents:
- The first term is \(3x^2 \sqrt{x^2 - 36}\).
- The second term involves several components: \( x^3 \), the fraction \(\frac{1}{2}\), the radical \((x^2 - 36)^{-1/2}\) raised to a negative fractional exponent, and multiplied by \( 2x \).
2. **Problem 2:**
This problem is an entirely different expression written methodically:
- The numerator is composed of two terms: \( 3x^2 (x^2 - 36) \) and \( x^4 \).
- The denominator is a square root: \( \sqrt{x^2 - 36} \).
Given the algebraic complexity, these problems likely pertain to calculus or pre-calculus topics for high school or university-level coursework, focusing on polynomial and radical expressions.
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