Question

Expand using suitable identity:
${(x-\frac{2}{3}y)}^3$

Answer 1

We need to expand ${(x-\frac{2}{3}y)}^3$

Suitable identities is $(x-y{)}^3=x^3-3x^{2}y+3x{y}^2-y^3$

The value of ${(x-\frac{2}{3}y)}^3$ is

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

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