Question 90262
First evaluate f(a+h)



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


{{{(a+h)^2+5=a^2+ha+ha+h^2+5}}} Foil


{{{(a+h)^2+5=a^2+2ha+h^2+5}}} Combine like terms



So {{{f(a+h)=a^2+2ha+h^2+5}}}


Now evaluate f(a)


{{{f(a)=a^2+5}}} plug in x=a


So {{{f(a)=a^2+5}}}


Now combine the two expressions



{{{f(a+h)-f(a)=(a^2+2ha+h^2+5)-(a^2+5)}}} Plug in the expressions previously solved for


{{{f(a+h)-f(a)=a^2+2ha+h^2+5-a^2-5}}} Distribute the negative


{{{f(a+h)-f(a)=2ha+h^2}}} Combine like terms