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(11−3)(11+3)left parenthesis 11 minus 3 right parenthesis left parenthesis 11 plus 3 right parenthesis(13−3)(19+3)
Answers
GPT-4o mini
To express the multiplication \( 13 \times 19 \) using the difference of two squares identity, we can rewrite it as:
\[
a^2 - b^2 = (a - b)(a + b)
\]
We can first find the average of 13 and 19, which is \( \frac{13 + 19}{2} = 16 \), and then notice that:
\[
13 = 16 - 3, \quad 19 = 16 + 3
\]
Now, we can express \( 13 \times 19 \) as follows:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]
This matches the difference of two squares identity since \( a = 16 \) and \( b = 3 \). Therefore, \( 13 \times 19 \) can be rewritten as:
\[
(16 - 3)(16 + 3)
\]
So the correct option is:
\[
(16 - 3)(16 + 3)
\]
\[
a^2 - b^2 = (a - b)(a + b)
\]
We can first find the average of 13 and 19, which is \( \frac{13 + 19}{2} = 16 \), and then notice that:
\[
13 = 16 - 3, \quad 19 = 16 + 3
\]
Now, we can express \( 13 \times 19 \) as follows:
\[
13 \times 19 = (16 - 3)(16 + 3)
\]
This matches the difference of two squares identity since \( a = 16 \) and \( b = 3 \). Therefore, \( 13 \times 19 \) can be rewritten as:
\[
(16 - 3)(16 + 3)
\]
So the correct option is:
\[
(16 - 3)(16 + 3)
\]