Which expression is equivalent to $$ \left(\frac{3}{2} p+1\right)\left(\frac{1}{2} p+3\right) $$ ? A. $$ 2 p^{2}+3 $$ B. $$ 4 p^{2}+3 $$ C. $$ \frac{3}{4} p^{2}+5 p+3 $$ D. $$ \frac{3}{4} p^{2}+10 p+3 $$

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To determine which expression is equivalent to $$ \left(\frac{3}{2} p + 1\right)\left(\frac{1}{2} p + 3\right) $$, let's expand the given expression step by step:

$$
\begin{align*}
\left(\frac{3}{2} p + 1\right)\left(\frac{1}{2} p + 3\right) &= \frac{3}{2} p \cdot \frac{1}{2} p + \frac{3}{2} p \cdot 3 + 1 \cdot \frac{1}{2} p + 1 \cdot 3 \
&= \frac{3}{4} p^2 + \frac{9}{2} p + \frac{1}{2} p + 3 \
&= \frac{3}{4} p^2 + \left(\frac{9}{2} + \frac{1}{2}\right) p + 3 \
&= \frac{3}{4} p^2 + 5 p + 3
\end{align*}
$$

Therefore, the equivalent expression is:

**C. $$ \frac{3}{4} p^{2} + 5 p + 3 $$**

**Answer:** C. $$ \frac{3}{4} p^{2}+5 p+3 $$
The equivalent expression is $$ \frac{3}{4} p^{2} + 5 p + 3 $$, which is option C.

Which expression is equivalent to ?
A.
B.
C.
D.

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