Question 35: Calculate the value of the expressions \({x^3} – {x^2}y + \frac{1}{3}x{y^2} – \frac{1}{{27}} {y^3}\) at x=2 and y=3

\(\begin{array}{l} {x^3} – {x^2}y + \frac{1}{3}x{y^2} – \frac{1}{{27}}{y ^3} = {x^3} – 3. {x^2}.\frac{1}{3}y + 3.x. {\left( {\frac{1}{3}y} \right) ^2} – {\left( {\frac{1}{3}y} \right)^3} = {\left( {x – \frac{1}{3}y} \right)^3}\ backslash \\ x = 2,y = 3 \to {\left( {x – \frac{1}{3}y} \right)^3} = {\left( {2 – \frac{1}{3 }.3} \right)^3} = {1^3} = 1 \end{array}\)