If the area of a rectangle is $8 x^{2} - 45 y^{2} + 18 x y$ and one of its sides is $4 x + 15 y$ , find the length of adjacent side.

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Solution

Let us factorize the given expression of area,
$\begin{matrix} 8 x^{2} + 18 x y - 45 y^{2} & = 8 x^{2} - 12 x y + 30 x y - 45 y^{2} = 4 x (2 x - 3 y) + 15 y (2 x - 3 y) = (4 x + 15) (2 x - 3 y) \end{matrix}$

It is given that the expression for one side is $4 x + 15 y$ hence the expression for the length of the other side will be, $2 x - 3 y .$

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