To find the product of \( 2.5d(3d^2 + 1.5d) \), we can use the distributive property (also known as the distributive law of multiplication).
- Distribute \( 2.5d \) to each term inside the parentheses:
\[ 2.5d \cdot 3d^2 + 2.5d \cdot 1.5d \]
- Calculate each term separately:
- For the first term:
\[ 2.5d \cdot 3d^2 = (2.5 \cdot 3)(d \cdot d^2) = 7.5d^{1+2} = 7.5d^3 \]
- For the second term:
\[ 2.5d \cdot 1.5d = (2.5 \cdot 1.5)(d \cdot d) = 3.75d^{1+1} = 3.75d^2 \]
- Combine the results:
\[ 7.5d^3 + 3.75d^2 \]
Therefore, the product of \( 2.5d(3d^2 + 1.5d) \) is
\[ \boxed{7.5d^3 + 3.75d^2} \]
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