Question

How can 13×19 be rewritten using the difference of two squares identity?(1 point)
Responses

(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

(10+3)(22−3)
left parenthesis 10 plus 3 right parenthesis left parenthesis 22 minus 3 right parenthesis

(11−3)(11+3)

Answer 1

To use the difference of two squares identity, we can rewrite \( 13 \times 19 \) as follows:

First, we note that:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]

This is because if we let \( a = 16 \) and \( b = 3 \), we can recognize that \( (16 - 3)(16 + 3) = a^2 - b^2 \) using the difference of squares identity, which gives us:
\[
16^2 - 3^2 = 256 - 9 = 247
\]
We check that \( 13 \times 19 = 247 \).

Thus, the correct response for rewriting \( 13 \times 19 \) using the difference of two squares identity is:

\[
(16 - 3)(16 + 3)
\]

So the answer is:
\[
\text{(16−3)(16+3)}
\]