To find the equation of volume \( V \) of a rectangular prism defined by the dimensions width \( w \), length \( l \), and height \( h \), we use the formula:
\[ V = l \times w \times h \]
Substituting the given expressions for \( l \), \( w \), and \( h \):
\[ V = (2x + 1)(x + 3)(x) \]
Now, we will expand this step by step.
First, expand \( (2x + 1)(x + 3) \):
\[ (2x + 1)(x + 3) = 2x^2 + 6x + 1x + 3 = 2x^2 + 7x + 3 \]
Now we have:
\[ V = (2x^2 + 7x + 3)(x) \]
Next, expand this expression:
\[ V = 2x^2 \cdot x + 7x \cdot x + 3 \cdot x = 2x^3 + 7x^2 + 3x \]
Now, we can write this in standard form (descending powers):
\[ V = 2x^3 + 7x^2 + 3x \]
In standard form with no spaces, the final answer is:
\[ V=2x^3+7x^2+3x \]