Question
Write the product of 10.5 and 20.5 using the difference of two squares identity.(1 point) Responses (15.5−5)(25.5−5) left parenthesis 15 point 5 minus 5 right parenthesis left parenthesis 25 point 5 minus 5 right parenthesis (15.5+5)(15.5−5) left parenthesis 15 point 5 plus 5 right parenthesis left parenthesis 15 point 5 minus 5 right parenthesis (15.5+5)(5.5+5) left parenthesis 15 point 5 plus 5 right parenthesis left parenthesis 5 point 5 plus 5 right parenthesis (5.5+5)(20.5−5)
Answers
GPT-4o mini
To find the product of \(10.5\) and \(20.5\) using the difference of squares identity, you can rewrite the numbers in the form \(a + b\) and \(a - b\).
Notice that:
\[
10.5 = 15.5 - 5 \quad \text{and} \quad 20.5 = 15.5 + 5
\]
Now we can express the product as:
\[
10.5 \times 20.5 = (15.5 - 5)(15.5 + 5)
\]
According to the difference of squares identity:
\[
(a - b)(a + b) = a^2 - b^2
\]
Here, \(a = 15.5\) and \(b = 5\). Therefore, we have:
\[
(15.5 - 5)(15.5 + 5) = 15.5^2 - 5^2
\]
Calculating that, we get:
\[
15.5^2 - 5^2 = 240.25 - 25 = 215.25
\]
Thus, the product of \(10.5\) and \(20.5\) can be expressed as:
\[
(15.5 - 5)(15.5 + 5)
\]
which is the correct application of the difference of two squares identity.
So, the correct response is:
\[
(15.5 - 5)(15.5 + 5)
\]
Notice that:
\[
10.5 = 15.5 - 5 \quad \text{and} \quad 20.5 = 15.5 + 5
\]
Now we can express the product as:
\[
10.5 \times 20.5 = (15.5 - 5)(15.5 + 5)
\]
According to the difference of squares identity:
\[
(a - b)(a + b) = a^2 - b^2
\]
Here, \(a = 15.5\) and \(b = 5\). Therefore, we have:
\[
(15.5 - 5)(15.5 + 5) = 15.5^2 - 5^2
\]
Calculating that, we get:
\[
15.5^2 - 5^2 = 240.25 - 25 = 215.25
\]
Thus, the product of \(10.5\) and \(20.5\) can be expressed as:
\[
(15.5 - 5)(15.5 + 5)
\]
which is the correct application of the difference of two squares identity.
So, the correct response is:
\[
(15.5 - 5)(15.5 + 5)
\]
Thats not one of the answers provided
GPT-4o mini
I apologize for the oversight. Let's examine the provided choices in order to select the correct one.
Given your request and the provided options, the correct expression for the product \(10.5 \times 20.5\) using the difference of squares identity can be applied as follows:
Start with:
- \(10.5 = 15.5 - 5\)
- \(20.5 = 15.5 + 5\)
Thus, we write:
\[
10.5 \times 20.5 = (15.5 - 5)(15.5 + 5)
\]
Out of the options provided, the one that corresponds to this expression is:
\[
(15.5 - 5)(15.5 + 5)
\]
Now, based on your options:
1. \( (15.5−5)(25.5−5) \)
2. \( (15.5+5)(15.5−5) \)
3. \( (15.5+5)(5.5+5) \)
4. \( (5.5+5)(20.5−5) \)
The correct expression derived is **not** in the options provided as they are all incorrect forms. However, if we are primarily checking for basic expressions, the closest option aligning with our \(a\) and \(b\) pattern would be:
- From the choices given, none correctly depict \( (15.5 - 5)(15.5 + 5) \).
If I had to select an alternative based on what might represent the framework we need, I could clarify that:
If we take:
\[
(15.5 + 5)(15.5 - 5)
\]
if defaulting to something like:
**"option 2: \( (15.5 + 5)(15.5 - 5) \)"**
this conveys the product correctly albeit in a negative form.
If you have any additional context or details for clarification, please share so I can assist you further!
Given your request and the provided options, the correct expression for the product \(10.5 \times 20.5\) using the difference of squares identity can be applied as follows:
Start with:
- \(10.5 = 15.5 - 5\)
- \(20.5 = 15.5 + 5\)
Thus, we write:
\[
10.5 \times 20.5 = (15.5 - 5)(15.5 + 5)
\]
Out of the options provided, the one that corresponds to this expression is:
\[
(15.5 - 5)(15.5 + 5)
\]
Now, based on your options:
1. \( (15.5−5)(25.5−5) \)
2. \( (15.5+5)(15.5−5) \)
3. \( (15.5+5)(5.5+5) \)
4. \( (5.5+5)(20.5−5) \)
The correct expression derived is **not** in the options provided as they are all incorrect forms. However, if we are primarily checking for basic expressions, the closest option aligning with our \(a\) and \(b\) pattern would be:
- From the choices given, none correctly depict \( (15.5 - 5)(15.5 + 5) \).
If I had to select an alternative based on what might represent the framework we need, I could clarify that:
If we take:
\[
(15.5 + 5)(15.5 - 5)
\]
if defaulting to something like:
**"option 2: \( (15.5 + 5)(15.5 - 5) \)"**
this conveys the product correctly albeit in a negative form.
If you have any additional context or details for clarification, please share so I can assist you further!