What is the possible expression for the dimension of the cuboid whose volume is given below?
$V o l u m e : 12 k y^{2} + 8 k y - 20 k$

4 k (3 y + 5) (y + 1)

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8 k (3 y + 5) (y + 1)

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4 k (3 y + 5) (y - 1)

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8 k (3 y + 5) (y - 1)

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Solution

The correct option is B $4 k (3 y + 5) (y - 1)$
$V o l u m e : 12 k y^{2} + 8 k y - 20 k = 4 k (3 y^{2} + 2 y - 5)$
$= 4 k (3 y^{2} - 3 y + 5 y - 5)$
$= 4 k [3 y (y - 1) + 5 (y - 1)]$
$= 4 k (3 y + 5) (y - 1)$
Hence the possible dimensions are $4 k, (3 y + 5), (y - 1)$

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

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