Question
How can 13×19 be rewritten using the difference of two squares identity?(1 point)
Responses
(10+3)(22−3)
left parenthesis 10 plus 3 right parenthesis left parenthesis 22 minus 3 right parenthesis
(16−3)(16+3)
left parenthesis 16 minus 3 right parenthesis left parenthesis 16 plus 3 right parenthesis
(13−3)(19+3)
left parenthesis 13 minus 3 right parenthesis left parenthesis 19 plus 3 right parenthesis
(11−3)(11+3)
Responses
(10+3)(22−3)
left parenthesis 10 plus 3 right parenthesis left parenthesis 22 minus 3 right parenthesis
(16−3)(16+3)
left parenthesis 16 minus 3 right parenthesis left parenthesis 16 plus 3 right parenthesis
(13−3)(19+3)
left parenthesis 13 minus 3 right parenthesis left parenthesis 19 plus 3 right parenthesis
(11−3)(11+3)
Answers
GPT-4o mini
To rewrite \( 13 \times 19 \) using the difference of two squares identity, you can express it in the form \( (a - b)(a + b) = a^2 - b^2 \).
We can find a suitable 'a' and 'b' such that:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]
Here, \( a = 16 \) and \( b = 3 \). When you multiply this out, you get:
\[
(16 - 3)(16 + 3) = 16^2 - 3^2 = 256 - 9 = 247
\]
And indeed, \( 13 \times 19 = 247 \).
Thus, the correct response is:
\((16 - 3)(16 + 3)\)
We can find a suitable 'a' and 'b' such that:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]
Here, \( a = 16 \) and \( b = 3 \). When you multiply this out, you get:
\[
(16 - 3)(16 + 3) = 16^2 - 3^2 = 256 - 9 = 247
\]
And indeed, \( 13 \times 19 = 247 \).
Thus, the correct response is:
\((16 - 3)(16 + 3)\)