Question

Find the product −3y(xy + y²) and find its value for x = 4 and y = 5.

Answer 1

To find the product, we will use distributive law as follows:​

\[- 3y\left( xy + y^2 \right)\]

\[ = - 3y \times xy + \left( - 3y \right) \times y^2 \]

\[ = - 3x y^{1 + 1} - 3 y^{1 + 2} \]

\[ = - 3x y^2 - 3 y^3\]

Substituting x = 4 and y = 5 in the result, we get:

\[- 3x y^2 - 3 y^3 \]

\[ = - 3\left( 4 \right) \left( 5 \right)^2 - 3 \left( 5 \right)^3 \]

\[ = - 3\left( 4 \right)\left( 25 \right) - 3\left( 125 \right)\]

\[ = - 300 - 375\]

\[ = - 675\]

Thus, the product is ( \[- 3x y^2 - 3 y^3\]), and its value for ​x = 4 and y = 5 is ( \[-\] 675).