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