We want to find \(\dfrac{f(x+a)-f(x)}{a}\)given that \(f(x)=x^2\).
To find \(f(x+a)\) we write \(f(x)=x^2\) in blank-parenthesis form \(f(~)=(~)^2\) and place \(x+a\) into each of the blank parentheses to get
\(f(x+a)=(x+a)^2=x^2+2ax+a^2\)
We already know that \(f(x)=x^2\), therefore
\begin{eqnarray*} \dfrac{f(x+a)-f(x)}{a}&=&\dfrac{x^2+2ax+a^2-x^2}{a}\\ &=&\dfrac{2ax+a^2}{a}\\ &=&\dfrac{a(2x+a)}{a}\\ &=&2x+a \end{eqnarray*}