Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.2: Adding And Subtracting Polynomials
Problem 39WE
Related questions
Question
![### Algebraic Expression Multiplication
#### Problem:
Multiply the following expression:
\[
(z - 4)^2
\]
#### Options:
1. \(\text{None of these}\)
2. \[z^2 - 8z - 16\]
3. \[z^2 + 8z + 16\]
4. \[z^2 + 16\]
5. \[z^2 - 16\]
The selected answer is:
\[z^2 - 16\]
#### Explanation:
To correctly multiply the expression \((z - 4)^2\), we need to apply the binomial theorem or the formula for the square of a binomial:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Here, \(a = z\) and \(b = 4\). Substituting these into the formula gives:
\[
(z - 4)^2 = z^2 - 2(z)(4) + 4^2 = z^2 - 8z + 16
\]
Therefore, the correct answer should be:
\[z^2 - 8z + 16\]
Given the correct steps, the answer marked as \(\text{None of these}\) is accurate since none of the listed answers match the correct result of \(z^2 - 8z + 16\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67f48f24-1057-4eac-87c6-4170e191b4a5%2Faad2c5e6-8e31-4a7c-9d61-9738c34ff846%2Fveaiqkw_processed.png&w=3840&q=75)
Transcribed Image Text:### Algebraic Expression Multiplication
#### Problem:
Multiply the following expression:
\[
(z - 4)^2
\]
#### Options:
1. \(\text{None of these}\)
2. \[z^2 - 8z - 16\]
3. \[z^2 + 8z + 16\]
4. \[z^2 + 16\]
5. \[z^2 - 16\]
The selected answer is:
\[z^2 - 16\]
#### Explanation:
To correctly multiply the expression \((z - 4)^2\), we need to apply the binomial theorem or the formula for the square of a binomial:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Here, \(a = z\) and \(b = 4\). Substituting these into the formula gives:
\[
(z - 4)^2 = z^2 - 2(z)(4) + 4^2 = z^2 - 8z + 16
\]
Therefore, the correct answer should be:
\[z^2 - 8z + 16\]
Given the correct steps, the answer marked as \(\text{None of these}\) is accurate since none of the listed answers match the correct result of \(z^2 - 8z + 16\).
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