Question

The volume of a prism is the product of its height and area of its base, V=Bh. A rectangular prism had a volume of 16y^4 + 16y^3 +48y^2 cubic units. Which could be the base area and height of the prism?

Answer 1

Volume = base × height

This is a multiplication relationship, so we need to manipulate the expression $16y^{4}+ 16y^{3}+ 48y^{2}$ into a product of two terms

We achieve this by factorising. 
The highest common factor of the constant 16, 16, and 48 is 16
The highest common factor of the variable $y^{4}, y^{3}$, and $y^{2}$ is $y^{2}$

So, factorising  $16y^{4}+ 16y^{3}+ 48y^{2}$ gives
$16 y^{2}( y^{2}+ y+3)$

Since the base of the square-based pyramid is a square, the expression of the base would be $16y^{2}$ (since this expression can be square rooted completely)

The height of the prism will be $y^{2}+y+3$