Answer:
[tex]\frac{-18z^{2}-37z-46}{z+2}[/tex]
Step-by-step explanation:
The given expression is
[tex]7-2z-4(\frac{z^{3}-z^{3}+4z^{2}+11z+14}{z+2})[/tex]
First, we have to apply distributive property
[tex]7-2z+\frac{-16z^{2}-44z-56}{z+2}=7-2z-\frac{16z^{2}+44z+56}{z+2}[/tex]
Then, we sum each term with the fraction, and solve the rest of operations, as follows
[tex]\frac{(7-2z)(z+2)-(16z^{2}+44z+56)}{z+2}\\\frac{7z+14-2z^{2}-4-16z^{2}-44z-56}{z+2}\\\frac{-18z^{2}-37z-46}{z+2}[/tex]
Therefore, the equivalent expression is
[tex]\frac{-18z^{2}-37z-46}{z+2}[/tex]
