Question
rite the product of 10.5 and 20.5 using the difference of two squares identity.(1 point)Responses(15.5+5)(15.5−5)left parenthesis 15 point 5 plus 5 right parenthesis left parenthesis 15 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)(25.5−5)
Answers
GPT-4o mini
To express the product of \( 10.5 \) and \( 20.5 \) using the difference of two squares identity, we start by rewriting the numbers in a form that is suitable for applying this identity.
The expression can be rewritten as:
\[
10.5 \times 20.5 = (15.5 - 5)(15.5 + 5)
\]
Here, \( a = 15.5 \) and \( b = 5 \).
Thus, the correct response using the difference of squares identity would be:
\[
(15.5 - 5)(15.5 + 5)
\]
This follows the form \( (a - b)(a + b) = a^2 - b^2 \).
So the answer is:
\[
(15.5 - 5)(15.5 + 5)
\]
The expression can be rewritten as:
\[
10.5 \times 20.5 = (15.5 - 5)(15.5 + 5)
\]
Here, \( a = 15.5 \) and \( b = 5 \).
Thus, the correct response using the difference of squares identity would be:
\[
(15.5 - 5)(15.5 + 5)
\]
This follows the form \( (a - b)(a + b) = a^2 - b^2 \).
So the answer is:
\[
(15.5 - 5)(15.5 + 5)
\]