Question
Find the product.
left parenthesis 9 x minus 5 right parenthesis squared
Question content area bottom
Part 1
left parenthesis 9 x minus 5 right parenthesis squaredequals
enter your response here
left parenthesis 9 x minus 5 right parenthesis squared
Question content area bottom
Part 1
left parenthesis 9 x minus 5 right parenthesis squaredequals
enter your response here
Answers
GPT-4o mini
To find the product of \((9x - 5)^2\), we will apply the formula for the square of a binomial, which is given by:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Here, \(a = 9x\) and \(b = 5\). Now we can calculate each part:
1. \(a^2 = (9x)^2 = 81x^2\)
2. \(b^2 = 5^2 = 25\)
3. \(2ab = 2 \cdot (9x) \cdot 5 = 90x\)
Putting these values into the formula:
\[
(9x - 5)^2 = a^2 - 2ab + b^2 = 81x^2 - 90x + 25
\]
Thus, the final answer is:
\[
(9x - 5)^2 = 81x^2 - 90x + 25
\]
\[
(a - b)^2 = a^2 - 2ab + b^2
\]
Here, \(a = 9x\) and \(b = 5\). Now we can calculate each part:
1. \(a^2 = (9x)^2 = 81x^2\)
2. \(b^2 = 5^2 = 25\)
3. \(2ab = 2 \cdot (9x) \cdot 5 = 90x\)
Putting these values into the formula:
\[
(9x - 5)^2 = a^2 - 2ab + b^2 = 81x^2 - 90x + 25
\]
Thus, the final answer is:
\[
(9x - 5)^2 = 81x^2 - 90x + 25
\]