To express [tex]\(15 + 30\)[/tex] as a multiple of a sum of whole numbers with no common factor, we start by examining the given options and performing the necessary calculations.
First, calculate [tex]\(15 + 30\)[/tex]:
[tex]\[
15 + 30 = 45
\][/tex]
We need to determine which of the given expressions is equal to 45.
Option A:
[tex]\[
2 \times (7.5 + 15) = 2 \times 22.5 = 45
\][/tex]
Here, the sum [tex]\( 7.5 + 15 = 22.5 \)[/tex] but [tex]\( 7.5 \)[/tex] is not a whole number. Thus, Option A is not valid.
Option B:
[tex]\[
3 \times (5 + 10) = 3 \times 15 = 45
\][/tex]
Here, the sum [tex]\( 5 + 10 = 15 \)[/tex]. Both 5 and 10 are whole numbers but they have the common factor 5, hence this expression does not meet the requirement. Thus, Option B is not valid.
Option C:
[tex]\[
5 \times (3 + 6) = 5 \times 9 = 45
\][/tex]
Here, the sum [tex]\( 3 + 6 = 9 \)[/tex]. Both 3 and 6 are whole numbers but they have the common factor 3, so this expression also does not meet the requirement. Thus, Option C is not valid.
Option D:
[tex]\[
15 \times (1 + 2) = 15 \times 3 = 45
\][/tex]
Here, the sum [tex]\( 1 + 2 = 3 \)[/tex]. Both 1 and 2 are whole numbers and they have no common factors other than 1. This option meets all the requirements.
Therefore, the correct answer is:
[tex]\[
\boxed{D}
\][/tex]
