Simplify (3/4x+2)^2

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

Combine fractions.

Combine $\frac{3}{4}$ and $x$ .

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

Rewrite ${(\frac{3 x}{4} + 2)}^{2}$ as $(\frac{3 x}{4} + 2) (\frac{3 x}{4} + 2)$ .

$(\frac{3 x}{4} + 2) (\frac{3 x}{4} + 2)$

Expand $(\frac{3 x}{4} + 2) (\frac{3 x}{4} + 2)$ using the FOIL Method.

Apply the distributive property.

$\frac{3 x}{4} (\frac{3 x}{4} + 2) + 2 (\frac{3 x}{4} + 2)$

Apply the distributive property.

$\frac{3 x}{4} \cdot \frac{3 x}{4} + \frac{3 x}{4} \cdot 2 + 2 (\frac{3 x}{4} + 2)$

Apply the distributive property.

$\frac{3 x}{4} \cdot \frac{3 x}{4} + \frac{3 x}{4} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Multiply $\frac{3 x}{4} \cdot \frac{3 x}{4}$ .

Multiply $\frac{3 x}{4}$ by $\frac{3 x}{4}$ .

$\frac{3 x (3 x)}{4 \cdot 4} + \frac{3 x}{4} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

Multiply $3$ by $3$ .

$\frac{9 x \cdot x}{4 \cdot 4} + \frac{3 x}{4} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

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

$\frac{9 (x^{1} x)}{4 \cdot 4} + \frac{3 x}{4} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

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

$\frac{9 (x^{1} x^{1})}{4 \cdot 4} + \frac{3 x}{4} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

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

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

Add $1$ and $1$ .

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

Multiply $4$ by $4$ .

$\frac{9 x^{2}}{16} + \frac{3 x}{4} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{9 x^{2}}{16} + \frac{3 x}{2 (2)} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

Cancel the common factor.

$\frac{9 x^{2}}{16} + \frac{3 x}{2 \cdot 2} \cdot 2 + 2 \frac{3 x}{4} + 2 \cdot 2$

Rewrite the expression.

$\frac{9 x^{2}}{16} + \frac{3 x}{2} + 2 \frac{3 x}{4} + 2 \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{9 x^{2}}{16} + \frac{3 x}{2} + 2 \frac{3 x}{2 (2)} + 2 \cdot 2$

Cancel the common factor.

$\frac{9 x^{2}}{16} + \frac{3 x}{2} + 2 \frac{3 x}{2 \cdot 2} + 2 \cdot 2$

Rewrite the expression.

$\frac{9 x^{2}}{16} + \frac{3 x}{2} + \frac{3 x}{2} + 2 \cdot 2$

Multiply $2$ by $2$ .

$\frac{9 x^{2}}{16} + \frac{3 x}{2} + \frac{3 x}{2} + 4$

Add $\frac{3 x}{2}$ and $\frac{3 x}{2}$ .

$\frac{9 x^{2}}{16} + 2 \frac{3 x}{2} + 4$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 x^{2}}{16} + 2 \frac{3 x}{2} + 4$

Rewrite the expression.

$\frac{9 x^{2}}{16} + 3 x + 4$

Simplify (3/4x+2)^2

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