What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

(i) Volume : 3x2–12x

(ii) Volume : 12ky2+8ky–20k

Solution:

(i) Volume : 3x2–12x

3x2–12x can be written as 3x(x–4) by taking 3x out of both the terms.

Possible expression for length = 3

Possible expression for breadth = x

Possible expression for height = (x–4)

(ii) Volume:
12ky2+8ky–20k

12ky2+8ky–20k can be written as 4k(3y2+2y–5) by taking 4k out of both the terms.

12ky2+8ky–20k = 4k(3y2+2y–5)

[Here, 3y2+2y–5 can be written as 3y2+5y–3y–5 using splitting the middle term method.]

= 4k(3y2+5y–3y–5)

= 4k[y(3y+5)–1(3y+5)]

= 4k(3y+5)(y–1)

Possible expression for length = 4k

Possible expression for breadth = (3y +5)

Possible expression for height = (y -1)