To simplify the expression [tex]\( 13 \sqrt{22b} - 10 \sqrt{22b} \)[/tex], we need to combine like terms.
In this case, both terms share the common factor [tex]\(\sqrt{22b}\)[/tex]. Here are the steps to simplify:
1. Identify the common factor in both terms:
[tex]\[ 13 \sqrt{22b} - 10 \sqrt{22b} \][/tex]
2. Factor out the common factor [tex]\(\sqrt{22b}\)[/tex]:
[tex]\[ (13 - 10) \sqrt{22b} \][/tex]
3. Perform the subtraction:
[tex]\[ 3 \sqrt{22b} \][/tex]
So, the simplified expression is:
[tex]\[ 3 \sqrt{22b} \][/tex]
Therefore, the expression [tex]\(13 \sqrt{22b} - 10 \sqrt{22b}\)[/tex] simplifies to [tex]\(3 \sqrt{22b}\)[/tex].
Hence, the correct answer is:
D. [tex]\(3 \sqrt{22 b}\)[/tex]
