7) \( \left(\frac{x}{3}+2\right)^{2} \)

To expand \( \left(\frac{x}{3}+2\right)^{2} \), you can use the binomial expansion formula or simply apply the distributive property (also known as the FOIL method). This expression can be rewritten as \( \left(a + b\right)^{2} \) where \( a = \frac{x}{3} \) and \( b = 2 \). When you expand, you get: \[ a^2 + 2ab + b^2 \] So calculating this gives: \[ \left(\frac{x}{3}\right)^{2} + 2 \cdot \frac{x}{3} \cdot 2 + 2^{2} \] \[ = \frac{x^{2}}{9} + \frac{4x}{3} + 4 \] Thus, the expanded form is: \[ \frac{x^{2}}{9} + \frac{4x}{3} + 4 \] And voilà! You've got your squared expression nicely simplified.