To solve the question of how [tex]\(13 \times 19\)[/tex] can be rewritten using the difference of two squares identity, we check each given expression one by one and see which one equals to [tex]\( 13 \times 19 \)[/tex].
Recall the difference of squares identity:
[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]
We'll evaluate the product for each provided pair and match it to [tex]\( 13 \times 19 = 247 \)[/tex].
1. First expression: [tex]\((13 - 3)(19 + 3)\)[/tex]
Simplify:
[tex]\[
(13 - 3) = 10
\][/tex]
[tex]\[
(19 + 3) = 22
\][/tex]
Evaluate:
[tex]\[
10 \times 22 = 220
\][/tex]
2. Second expression: [tex]\((10 + 3)(22 - 3)\)[/tex]
Simplify:
[tex]\[
(10 + 3) = 13
\][/tex]
[tex]\[
(22 - 3) = 19
\][/tex]
Evaluate:
[tex]\[
13 \times 19 = 247
\][/tex]
3. Third expression: [tex]\((16 - 3)(16 + 3)\)[/tex]
Simplify:
[tex]\[
(16 - 3) = 13
\][/tex]
[tex]\[
(16 + 3) = 19
\][/tex]
Evaluate:
[tex]\[
13 \times 19 = 247
\][/tex]
4. Fourth expression: [tex]\((11 - 3)(11 + 3)\)[/tex]
Simplify:
[tex]\[
(11 - 3) = 8
\][/tex]
[tex]\[
(11 + 3) = 14
\][/tex]
Evaluate:
[tex]\[
8 \times 14 = 112
\][/tex]
Only the second and third expressions correctly match the product [tex]\( 13 \times 19 = 247 \)[/tex]. Hence, the correct ways to rewrite [tex]\( 13 \times 19 \)[/tex] using the difference of two squares identity are:
[tex]\[
(10 + 3)(22 - 3) \quad \text{and} \quad (16 - 3)(16 + 3)
\][/tex]
