To determine an expression equivalent to [tex]\(13 \sqrt{22 b} - 10 \sqrt{22 b}\)[/tex], we will combine like terms.
1. First, note that both terms [tex]\(13 \sqrt{22 b}\)[/tex] and [tex]\(10 \sqrt{22 b}\)[/tex] have the common factor [tex]\(\sqrt{22 b}\)[/tex]:
[tex]\[
13 \sqrt{22 b} - 10 \sqrt{22 b}
\][/tex]
2. Factor out the common factor of [tex]\(\sqrt{22 b}\)[/tex]:
[tex]\[
(13 - 10) \sqrt{22 b}
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
3 \sqrt{22 b}
\][/tex]
So, the expression [tex]\(13 \sqrt{22 b} - 10 \sqrt{22 b}\)[/tex] simplifies to [tex]\(3 \sqrt{22 b}\)[/tex].
Therefore, the correct answer is:
D. [tex]\(3 \sqrt{22 b}\)[/tex]
