Let's simplify the expression [tex]\(10 \sqrt{2y} + 5 \sqrt{2y} + 3 \sqrt{2y}\)[/tex] step by step.
1. Identify the like terms: In the expression [tex]\(10 \sqrt{2y} + 5 \sqrt{2y} + 3 \sqrt{2y}\)[/tex], all the terms contain the common factor [tex]\(\sqrt{2y}\)[/tex].
2. Combine the coefficients of like terms:
[tex]\[
(10 + 5 + 3) \sqrt{2y}
\][/tex]
3. Perform the addition within the parentheses:
[tex]\[
10 + 5 + 3 = 18
\][/tex]
4. Multiply the combined coefficient by the common factor:
[tex]\[
18 \sqrt{2y}
\][/tex]
Thus, the simplified form of the expression [tex]\(10 \sqrt{2y} + 5 \sqrt{2y} + 3 \sqrt{2y}\)[/tex] is [tex]\(18 \sqrt{2y}\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{18 \sqrt{2y}}
\][/tex]
