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
(13−3)(19+3)
left parenthesis 13 minus 3 right parenthesis left parenthesis 19 plus 3 right parenthesis
(16−3)(16+3)
left parenthesis 16 minus 3 right parenthesis left parenthesis 16 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
(13−3)(19+3)
left parenthesis 13 minus 3 right parenthesis left parenthesis 19 plus 3 right parenthesis
(16−3)(16+3)
left parenthesis 16 minus 3 right parenthesis left parenthesis 16 plus 3 right parenthesis
(11−3)(11+3)
Answers
GPT-4o mini
The difference of squares identity states that \( a^2 - b^2 = (a - b)(a + b) \).
To apply this to \( 13 \times 19 \), we can express this product in the form of a difference of squares. We notice that \( 16^2 = 256 \), which can be broken down into:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]
This allows us to use \( a = 16 \) and \( b = 3 \), resulting in:
\[
16^2 - 3^2 = 256 - 9 = 247
\]
Therefore, \( 13 \times 19 \) can be rewritten using the difference of squares identity as:
**(16−3)(16+3)**
\[
\text{(16 - 3)(16 + 3)}
\]
This is the correct response.
To apply this to \( 13 \times 19 \), we can express this product in the form of a difference of squares. We notice that \( 16^2 = 256 \), which can be broken down into:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]
This allows us to use \( a = 16 \) and \( b = 3 \), resulting in:
\[
16^2 - 3^2 = 256 - 9 = 247
\]
Therefore, \( 13 \times 19 \) can be rewritten using the difference of squares identity as:
**(16−3)(16+3)**
\[
\text{(16 - 3)(16 + 3)}
\]
This is the correct response.