Given that g(p)=p-2 and
[tex]h(p)=p^3+4p^2-2[/tex]
Now we have to evaluate g(p)*h(p) by modeling or by using the distributive property.
We know that g(p)*h(p) means just multiply expressions of g(p) with h(p)
which can be shown as following:
[tex]g(p)*h(p)=(p^3+4p^2-2)(p-2)[/tex]
Apply distributive property
[tex]g(p)*h(p)=p(p^3+4p^2-2)-2(p^3+4p^2-2)[/tex]
[tex]g(p)*h(p)=p^4+4p^3-2p-2p^3-8p^2+4[/tex]
[tex]g(p)*h(p)=p^4+2p^3-2p-8p^2+4[/tex]
[tex]g(p)*h(p)=p^4+2p^3-8p^2-2p+4[/tex]
Hence final answer is [tex]g(p)*h(p)=p^4+2p^3-8p^2-2p+4[/tex]
