By using standard formulae, expand the following:

$\Big(\dfrac{1}{2}x + \dfrac{2}{3}y\Big)^2$

$\Big(\dfrac{1}{2}x + \dfrac{2}{3}y\Big)^2 = \Big(\dfrac{1}{2}x\Big)^2 + 2\Big(\dfrac{1}{2}x\Big)\Big(\dfrac{2}{3}y\Big) + \Big(\dfrac{2}{3}y\Big)^2 \\[1em] = \dfrac{1}{4}x^2 + \dfrac{2}{3}xy + \dfrac{4}{9}y^2$