Volume = base × height
This is a multiplication relationship, so we need to manipulate the expression [tex]16y^{4}+ 16y^{3}+ 48y^{2} [/tex] 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 [tex] y^{4}, y^{3} [/tex], and [tex] y^{2} [/tex] is [tex] y^{2} [/tex]
So, factorising [tex]16y^{4}+ 16y^{3}+ 48y^{2} [/tex] gives
[tex]16 y^{2}( y^{2}+ y+3)[/tex]
Since the base of the square-based pyramid is a square, the expression of the base would be [tex]16y^{2} [/tex] (since this expression can be square rooted completely)
The height of the prism will be [tex] y^{2}+y+3 [/tex]
