Find possible expressions for the length, breadth, and heights of each of the following cuboids whose volumes are given by the following expressions in cubic units.
(A) $6a^2 - 24b^2$
(B) $3ps^2 - 15ps + 12p$

$$\text{(A)}\quad6a^2-24b^2=6(a^2-4b^2)=6(a-2b)(a+2b)$$

Possible dimensions: Length = 6,

Breadth = (a - 2b), Height = (a + 2b)

$$\text{(B)} \quad 3ps^2 - 15ps + 12p = 3p(s^2 - 5s + 4)$$

$$= 3p(s - 1)(s - 4)$$

Possible dimensions: $Length=3p$,

$\text{Breadth} = (s - 1)$, $\text{Height} = (s - 4)$