Question

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

(11−3)(11+3)
left parenthesis 11 minus 3 right parenthesis left parenthesis 11 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

(16−3)(16+3)

Answer 1

To rewrite \( 13 \times 19 \) using the difference of two squares identity, we need to express it in the form \( (a - b)(a + b) = a^2 - b^2 \).

First, we can express \( 13 \times 19 \) as follows:

1. Calculate the average of 13 and 19:
\[
\text{Average} = \frac{13 + 19}{2} = 16
\]

2. Calculate the difference from the average:
\[
13 = 16 - 3 \quad \text{and} \quad 19 = 16 + 3
\]

So, we can rewrite \( 13 \times 19 \) as:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]

Thus, the correct response is:
**(16−3)(16+3)**.