### Educational Content: Simplifying Expressions **Problem Statement:** Rewrite the following expression without parentheses and simplify your answer as much as possible: \[ -8w^2(4w^3 - 7w^2 - 9w) \] **Solution Guide:** 1. **Distribute the term outside the parentheses:** - Multiply \(-8w^2\) by each term inside the parentheses: - \(-8w^2 \times 4w^3\) - \(-8w^2 \times (-7w^2)\) - \(-8w^2 \times (-9w)\) 2. **Calculate each multiplication:** - \(-8w^2 \times 4w^3 = -32w^{5}\) - \(-8w^2 \times (-7w^2) = 56w^{4}\) - \(-8w^2 \times (-9w) = 72w^{3}\) 3. **Write the simplified expression:** \[ -32w^5 + 56w^4 + 72w^3 \] This process involves applying the distributive property and combining like terms if necessary. The final answer is already simplified as no further like terms are present for combining.
### Educational Content: Simplifying Expressions **Problem Statement:** Rewrite the following expression without parentheses and simplify your answer as much as possible: \[ -8w^2(4w^3 - 7w^2 - 9w) \] **Solution Guide:** 1. **Distribute the term outside the parentheses:** - Multiply \(-8w^2\) by each term inside the parentheses: - \(-8w^2 \times 4w^3\) - \(-8w^2 \times (-7w^2)\) - \(-8w^2 \times (-9w)\) 2. **Calculate each multiplication:** - \(-8w^2 \times 4w^3 = -32w^{5}\) - \(-8w^2 \times (-7w^2) = 56w^{4}\) - \(-8w^2 \times (-9w) = 72w^{3}\) 3. **Write the simplified expression:** \[ -32w^5 + 56w^4 + 72w^3 \] This process involves applying the distributive property and combining like terms if necessary. The final answer is already simplified as no further like terms are present for combining.
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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![### Educational Content: Simplifying Expressions
**Problem Statement:**
Rewrite the following expression without parentheses and simplify your answer as much as possible:
\[ -8w^2(4w^3 - 7w^2 - 9w) \]
**Solution Guide:**
1. **Distribute the term outside the parentheses:**
- Multiply \(-8w^2\) by each term inside the parentheses:
- \(-8w^2 \times 4w^3\)
- \(-8w^2 \times (-7w^2)\)
- \(-8w^2 \times (-9w)\)
2. **Calculate each multiplication:**
- \(-8w^2 \times 4w^3 = -32w^{5}\)
- \(-8w^2 \times (-7w^2) = 56w^{4}\)
- \(-8w^2 \times (-9w) = 72w^{3}\)
3. **Write the simplified expression:**
\[
-32w^5 + 56w^4 + 72w^3
\]
This process involves applying the distributive property and combining like terms if necessary. The final answer is already simplified as no further like terms are present for combining.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe83af5ed-54b5-49f8-a30b-03cf66c2f19a%2F12a63c4a-96e6-4dea-a0bc-9b79db01806e%2Fsam7ifj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content: Simplifying Expressions
**Problem Statement:**
Rewrite the following expression without parentheses and simplify your answer as much as possible:
\[ -8w^2(4w^3 - 7w^2 - 9w) \]
**Solution Guide:**
1. **Distribute the term outside the parentheses:**
- Multiply \(-8w^2\) by each term inside the parentheses:
- \(-8w^2 \times 4w^3\)
- \(-8w^2 \times (-7w^2)\)
- \(-8w^2 \times (-9w)\)
2. **Calculate each multiplication:**
- \(-8w^2 \times 4w^3 = -32w^{5}\)
- \(-8w^2 \times (-7w^2) = 56w^{4}\)
- \(-8w^2 \times (-9w) = 72w^{3}\)
3. **Write the simplified expression:**
\[
-32w^5 + 56w^4 + 72w^3
\]
This process involves applying the distributive property and combining like terms if necessary. The final answer is already simplified as no further like terms are present for combining.
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