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:**
What value of \( b \) makes the equation below true? Explain or show how you know.
\[ (10x - 7)(8x + 3) = 80x^2 + bx - 21 \]
**Explanation:**
To find the value of \( b \), first expand the left side of the equation:
\[
(10x - 7)(8x + 3)
\]
Applying the distributive property (FOIL method):
1. Multiply the first terms: \(10x \times 8x = 80x^2\)
2. Multiply the outer terms: \(10x \times 3 = 30x\)
3. Multiply the inner terms: \(-7 \times 8x = -56x\)
4. Multiply the last terms: \(-7 \times 3 = -21\)
Combine these results:
\[
80x^2 + 30x - 56x - 21
\]
Combine like terms:
\[
80x^2 - 26x - 21
\]
Now, compare this with the equation on the right:
\[
80x^2 + bx - 21
\]
By comparing the two expressions, we find:
\[
b = -26
\]
Thus, the value of \( b \) that makes the equation true is \( -26 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63560604-4e69-491e-ad91-655471205395%2F5d853aba-ded2-4a13-b879-5e537601bc5b%2Feskqxo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What value of \( b \) makes the equation below true? Explain or show how you know.
\[ (10x - 7)(8x + 3) = 80x^2 + bx - 21 \]
**Explanation:**
To find the value of \( b \), first expand the left side of the equation:
\[
(10x - 7)(8x + 3)
\]
Applying the distributive property (FOIL method):
1. Multiply the first terms: \(10x \times 8x = 80x^2\)
2. Multiply the outer terms: \(10x \times 3 = 30x\)
3. Multiply the inner terms: \(-7 \times 8x = -56x\)
4. Multiply the last terms: \(-7 \times 3 = -21\)
Combine these results:
\[
80x^2 + 30x - 56x - 21
\]
Combine like terms:
\[
80x^2 - 26x - 21
\]
Now, compare this with the equation on the right:
\[
80x^2 + bx - 21
\]
By comparing the two expressions, we find:
\[
b = -26
\]
Thus, the value of \( b \) that makes the equation true is \( -26 \).
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