Answer:
The Volume of the cube is
\((64x^{6}+144x^{4}+108x^{2}+27)\)
Step-by-step explanation:
we know that
The volume of a cube is equal to
\(V=s^{3}\)
where
s is the length side of the cube
In this problem we have
\(s=(4x^{2} +3)\)
Substitute
\(V=(4x^{2} +3)^{3}\)
Remember that
\((4x^{2} +3)^{3}=(4x^{2} +3)^{2}(4x^{2} +3)\)
\((4x^{2} +3)^{2}(4x^{2} +3)=[16x^{4}+24x^{2} +9]( 4x^{2} +3)\)
\(=64x^{6}+48x^{4}+96x^{4}+72x^{2}+36x^{2}+27\)
Combine like terms
\(=64x^{6}+144x^{4}+108x^{2}+27\)
