Question 183683
I'll do the first one to get you started.



{{{f(x)=2x^4+5}}} Start with the given function.



{{{f(a+h)=2(a+h)^4+5}}} Plug in {{{x=a+h}}}



{{{f(a+h)=2(a+h)^2(a+h)^2+5}}} Break up {{{(a+h)^4}}} to get {{{(a+h)^2(a+h)^2}}}



{{{f(a+h)=2(a^2+2ah+h^2)(a^2+2ah+h^2)+5}}} FOIL



{{{f(a+h)=2(a^2(a^2+2ah+h^2)+2ah(a^2+2ah+h^2)+h^2(a^2+2ah+h^2))+5}}} Expand



{{{f(a+h)=2((a^4+2a^3h+a^2h^2)+(2a^3h+4a^2h^2+2ah^3)+(a^2h^2+2ah^3+h^4))+5}}} Distribute




{{{f(a+h)=2(a^4+4a^3h+6a^2h^2+4ah^3+h^4)+5}}} Combine like terms.



{{{f(a+h)=2a^4+8a^3h+12a^2h^2+8ah^3+2h^4+5}}} Distribute




So the answer is {{{f(a+h)=2a^4+8a^3h+12a^2h^2+8ah^3+2h^4+5}}}