Simplify (3/2p+1)(1/2p+3)

$(\frac{3}{2} p + 1) (\frac{1}{2} p + 3)$

Combine fractions.

Combine $\frac{3}{2}$ and $p$ .

$(\frac{3 p}{2} + 1) (\frac{1}{2} p + 3)$

Combine $\frac{1}{2}$ and $p$ .

$(\frac{3 p}{2} + 1) (\frac{p}{2} + 3)$

Expand $(\frac{3 p}{2} + 1) (\frac{p}{2} + 3)$ using the FOIL Method.

Apply the distributive property.

$\frac{3 p}{2} (\frac{p}{2} + 3) + 1 (\frac{p}{2} + 3)$

Apply the distributive property.

$\frac{3 p}{2} \cdot \frac{p}{2} + \frac{3 p}{2} \cdot 3 + 1 (\frac{p}{2} + 3)$

Apply the distributive property.

$\frac{3 p}{2} \cdot \frac{p}{2} + \frac{3 p}{2} \cdot 3 + 1 \frac{p}{2} + 1 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Multiply $\frac{3 p}{2} \cdot \frac{p}{2}$ .

Multiply $\frac{3 p}{2}$ by $\frac{p}{2}$ .

$\frac{3 p \cdot p}{2 \cdot 2} + \frac{3 p}{2} \cdot 3 + 1 \frac{p}{2} + 1 \cdot 3$

Raise $p$ to the power of $1$ .

$\frac{3 (p^{1} p)}{2 \cdot 2} + \frac{3 p}{2} \cdot 3 + 1 \frac{p}{2} + 1 \cdot 3$

Raise $p$ to the power of $1$ .

$\frac{3 (p^{1} p^{1})}{2 \cdot 2} + \frac{3 p}{2} \cdot 3 + 1 \frac{p}{2} + 1 \cdot 3$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 p^{1 + 1}}{2 \cdot 2} + \frac{3 p}{2} \cdot 3 + 1 \frac{p}{2} + 1 \cdot 3$

Add $1$ and $1$ .

$\frac{3 p^{2}}{2 \cdot 2} + \frac{3 p}{2} \cdot 3 + 1 \frac{p}{2} + 1 \cdot 3$

Multiply $2$ by $2$ .

$\frac{3 p^{2}}{4} + \frac{3 p}{2} \cdot 3 + 1 \frac{p}{2} + 1 \cdot 3$

Multiply $\frac{3 p}{2} \cdot 3$ .

Combine $\frac{3 p}{2}$ and $3$ .

$\frac{3 p^{2}}{4} + \frac{3 p \cdot 3}{2} + 1 \frac{p}{2} + 1 \cdot 3$

Multiply $3$ by $3$ .

$\frac{3 p^{2}}{4} + \frac{9 p}{2} + 1 \frac{p}{2} + 1 \cdot 3$

Multiply $\frac{p}{2}$ by $1$ .

$\frac{3 p^{2}}{4} + \frac{9 p}{2} + \frac{p}{2} + 1 \cdot 3$

Multiply $3$ by $1$ .

$\frac{3 p^{2}}{4} + \frac{9 p}{2} + \frac{p}{2} + 3$

Combine the numerators over the common denominator.

$\frac{3 p^{2}}{4} + \frac{9 p + p}{2} + 3$

Add $9 p$ and $p$ .

$\frac{3 p^{2}}{4} + \frac{10 p}{2} + 3$

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10 p$ .

$\frac{3 p^{2}}{4} + \frac{2 (5 p)}{2} + 3$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{3 p^{2}}{4} + \frac{2 (5 p)}{2 (1)} + 3$

Cancel the common factor.

$\frac{3 p^{2}}{4} + \frac{2 (5 p)}{2 \cdot 1} + 3$

Rewrite the expression.

$\frac{3 p^{2}}{4} + \frac{5 p}{1} + 3$

Divide $5 p$ by $1$ .

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

Simplify (3/2p+1)(1/2p+3)

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