The given function is expressed as
f(x) = x^2 + 2x
To determine f(a + h) - f(a), we would substitute x = a + h into the function and also x = a int the function. After this, we would carry out the neccessary subtraction.
f(a + h) = (a + h)^2 + 2(a + h)
f(a + h) = (a + h)(a + h) + 2a +2h
f(a + h) = a^2 + ah + ah + h^2 + 2a + 2h
f(a + h) = a^2 + 2ah + h^2+ 2a + 2h
Also
f(a) = a^2 + 2a
Therefore,
f(a + h) - f(a) = a^2 + 2ah + h^2+ 2a + 2h - (a^2 + 2a)
f(a + h) - f(a) = a^2 + 2ah + h^2+ 2a + 2h - a^2 - 2a
f(a + h) - f(a) = a^2 - a^2 + 2ah + h^2 + 2h + 2a - 2a
f(a + h) - f(a) = 2ah + h^2 + 2h
f(a + h) - f(a) = h^2 + 2ah + 2h
Option D is correct