What are the possible expressions for the dimensions of a cuboid whose volume is
given below ?
Volume = 12ky²+8ky-20k

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Solution

Given, volume of the cuboid is

$24 k y^{2} - 4 k y - 8 k \Rightarrow 4 k (6 y^{2} - y - 2) \Rightarrow 4 k (6 y^{2} + 3 y - 4 y - 2) \Rightarrow 4 k [3 y (2 y + 1) - 2 (2 y + 1)] \Rightarrow 4 k (3 y - 2) (2 y + 1)$ .

Thus, the possible dimensions of the cuboid are 4k, 3y - 2 and 2y + 1.

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12 k y^{2} + 8 k y - 20 k

V o l u m e : 12 k y^{2} + 8 k y - 20 k

What are the possible expressions for the dimensions of the cuboid whose volumes are given below?
(i) Volume: ${3 x}^{2} - 12 x$

(ii) Volume: $12 k y^{2} + 8 k y - 20 k$

What are the possible expressions for the dimensions of cuboid , whose volume is : 12ky^2 +8ky- 20 k?

\begin{matrix} \begin{matrix} V o l u m e : 3 x^{2} - 12 x \end{matrix} (i) \end{matrix} \begin{matrix} \begin{matrix} V o l u m e : 12 k y^{2} + 8 k y - 20 k \end{matrix} (i i) \end{matrix}

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