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
(5.5+5)(20.5−5)
left parenthesis 5 point 5 plus 5 right parenthesis left parenthesis 20 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
(15.5+5)(15.5−5)
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
(5.5+5)(20.5−5)
left parenthesis 5 point 5 plus 5 right parenthesis left parenthesis 20 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
(15.5+5)(15.5−5)
Answers
GPT-4o mini
To express the product of 10.5 and 20.5 using the difference of two squares identity, we can rewrite these numbers:
- Let's denote \(x = 15.5\) (which is the midpoint between 10.5 and 20.5).
- Then, we express 10.5 as \(x - 5\) and 20.5 as \(x + 5\).
The product can then be written as:
\[ (x - 5)(x + 5) \]
According to the difference of squares identity, this product is equal to:
\[ x^2 - 5^2 \]
Substituting back in for \(x\):
\[ (15.5 - 5)(15.5 + 5) \]
Thus, the correct response is:
\[
(15.5 + 5)(15.5 - 5)
\]
- Let's denote \(x = 15.5\) (which is the midpoint between 10.5 and 20.5).
- Then, we express 10.5 as \(x - 5\) and 20.5 as \(x + 5\).
The product can then be written as:
\[ (x - 5)(x + 5) \]
According to the difference of squares identity, this product is equal to:
\[ x^2 - 5^2 \]
Substituting back in for \(x\):
\[ (15.5 - 5)(15.5 + 5) \]
Thus, the correct response is:
\[
(15.5 + 5)(15.5 - 5)
\]