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