To find the volume \( V \) of the rectangular prism, we can use the formula:
\[ V = l \cdot w \cdot h \]
Given the dimensions:
- Length \( l = 5a \)
- Width \( w = 2a \)
- Height \( h = a^3 - 3a^2 + a \)
Now we can substitute these values into the volume formula:
\[ V = (5a) \cdot (2a) \cdot (a^3 - 3a^2 + a) \]
First, calculate the product of the length and width:
\[ 5a \cdot 2a = 10a^2 \]
Now we need to multiply this result by the height:
\[ V = 10a^2 \cdot (a^3 - 3a^2 + a) \]
Distributing \( 10a^2 \) into the polynomial:
\[ V = 10a^2 \cdot a^3 - 10a^2 \cdot 3a^2 + 10a^2 \cdot a \] \[ V = 10a^{5} - 30a^{4} + 10a^{3} \]
Thus, the volume of the rectangular prism is:
\[ \boxed{10a^5 - 30a^4 + 10a^3} \]
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