Question

Solve: ${[x-\frac{2}{3}y]}^3$

Answer 1

${[x-\frac{2}{3}y]}^3$

$\therefore (a-b{)}^3=a^3-b^3-3a^{2}b+3a{b}^2$

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

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

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