Question

Write the cubes in expanded form ${[x-\frac{2}{3}y]}^3$

Answer 1

Using\quad ${(a-b)}^3=a^3-b^3-3ab(a-b)$

Take\quad $a=x,b=\frac{2}{3}y$

${(x-\frac{2}{3}y)}^3=x^3-{\left(\frac{2}{3}y\right)}^3-\left(3x\right)\left(\frac{2}{3}y\right)(x-\frac{2}{3}y)$

$=x^3-\frac{8}{27}{y}^3-2xy(x-\frac{2}{3}y)$

$=x^3-\frac{8}{27}{y}^3-2xy\left(x\right)-2xy(-\frac{2}{3}y)$

$=x^3-\frac{8}{27}{y}^3-x^{2}y+\frac{4}{3}x{y}^2$