Question

Question 16
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
$\begin{array}{c}\begin{array}{c}Volume:3x^2-12x\end{array}\\ \left(i\right)\end{array}\begin{array}{c}\begin{array}{c}Volume:12k{y}^2+8ky-20k\end{array}\\ \left(ii\right)\end{array}$

Answer 1

$\left(i\right)Volumeofcuboid=abc=3x^2-12x=3x(x-4)$

$\therefore \text{3, x(x-4) are the three factors.}$
So, these can be the three dimensions.

$\left(ii\right)Volumeofcuboid=abc=12k{y}^2+8ky-20k=4k(3y^2+2y-5)=4k\left[3y(y-1)+5(y-1)\right]=4k(y-1)(3y+5)$

$\therefore \text{4k, (y-1) and (3y+5) are the three factors.}$
Hence, these can be the three dimensions.