Simplify ((x+3x)/(y+2y))^2

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

Add $x$ and $3 x$ .

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

Add $y$ and $2 y$ .

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{4 x}{3 y}$ .

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

Apply the product rule to $4 x$ .

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

Apply the product rule to $3 y$ .

$\frac{4^{2} x^{2}}{3^{2} y^{2}}$

Raise $4$ to the power of $2$ .

$\frac{16 x^{2}}{3^{2} y^{2}}$

Raise $3$ to the power of $2$ .

$\frac{16 x^{2}}{9 y^{2}}$