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

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Solution

Volume : 12ky² + 8ky – 20k

Since, volume is product of length, breadth and height therefore by factorizing the given volume, we can know the length, breadth and height of the cuboid. 12ky²

+ 8ky – 20k

= 4k(3y² + 2y – 5)

[By middle term splitting]

= 4k(3y² +5y-3y-5)

= 4k[y(3y+5)-1(3y+ 5)]= 4k

(3y +5) (y – 1)

Hence,possible expression for length = 4k

Possible expression for breadth = (3y +5)

Possible expression for height = (y – 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?
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(ii) Volume: $12 k y^{2} + 8 k y - 20 k$

\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}

12 k x^{2} + 8 k x - 20 k ?

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