Question 46: Multiply \( \begin{array}{I} \left( { – {x^2}{y^3} + \frac{1}{2}x{y^2} – 2xy + 1} \right).x{y^2} \end{array} \) we get:

\( \begin{array}{I} \left( { – {x^2}{y^3} + \frac{1}{2}x{y^2} – 2xy + 1} \right).x {y^2}\\ = \left( { – {x^2}{y^3}} \right).x{y^2} + \frac{1}{2}x{y^2}. x{y^2} – 2xy.x{y^2} + 1.x{y^2}\\ = – {x^2}{y^5} + \frac{1}{2}{x^ 2}{y^4} – 2{x^2}{y^3} + x{y^2} \end{array} \)