How can 13×19 be rewritten using the difference of two squares identity?(1 point) Responses (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) left parenthesis 11 minus 3 right parenthesis left parenthesis 11 plus 3 right parenthesis (16−3)(16+3)

1 answer

To rewrite \( 13 \times 19 \) using the difference of two squares identity, we start by noticing that \( 13 \) and \( 19 \) can be expressed in terms of \( 16 \) (the average of \( 13 \) and \( 19 \)):

We can represent \( 13 \) as \( 16 - 3 \) and \( 19 \) as \( 16 + 3 \). Therefore:

\[ 13 \times 19 = (16 - 3)(16 + 3) \]

Using the difference of squares identity, which states that \( (a - b)(a + b) = a^2 - b^2 \), we can see that this expression matches the form.

Therefore, the correct response is:

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