Write the following cube in expanded form: $\left[x-\frac{2}{3} y\right]^{3}$

(N/A) To expand $\left(x-\frac{2}{3} y\right)^{3}$,we use the algebraic identity: $(a-b)^{3} = a^{3} - b^{3} - 3ab(a-b)$.
Here,$a = x$ and $b = \frac{2}{3}y$.
Substituting these values into the identity:
$\left(x-\frac{2}{3} y\right)^{3} = x^{3} - \left(\frac{2}{3} y\right)^{3} - 3(x)\left(\frac{2}{3} y\right)\left(x-\frac{2}{3} y\right)$
$= x^{3} - \frac{8}{27} y^{3} - 2xy\left(x-\frac{2}{3} y\right)$
$= x^{3} - \frac{8}{27} y^{3} - 2x^{2}y + \left(2xy \cdot \frac{2}{3}y\right)$
$= x^{3} - \frac{8}{27} y^{3} - 2x^{2}y + \frac{4}{3}xy^{2}$