To solve the expression \( 13 \sqrt{22 b} - 10 \sqrt{22 b} \), let's break it down step-by-step.
First, let's identify that both terms in the expression share the common factor \( \sqrt{22 b} \):
[tex]\[ 13 \sqrt{22 b} - 10 \sqrt{22 b} \][/tex]
This expression can be factored by pulling out the common term \( \sqrt{22 b} \):
[tex]\[ \left( 13 - 10 \right) \sqrt{22 b} \][/tex]
Next, we simplify the expression inside the parentheses:
[tex]\[ \left( 13 - 10 \right) = 3 \][/tex]
Substituting this back in gives:
[tex]\[ 3 \sqrt{22 b} \][/tex]
Thus, the simplified form of the given expression \( 13 \sqrt{22 b} - 10 \sqrt{22 b} \) is:
[tex]\[ 3 \sqrt{22 b} \][/tex]
Therefore, the equivalent expression to \( 13 \sqrt{22 b} - 10 \sqrt{22 b} \) is:
[tex]\[ \boxed{3 \sqrt{22 b}} \][/tex]
Hence, the correct answer is:
D. [tex]\( 3 \sqrt{22 b} \)[/tex]
