For f(x)=2x^2-4x+3 find f(x+h)-f(x)
f(x)=2x^2-4x+3
f(x+h) = 2(x+h)^2 - 4(x+h) + 3
= 2(x^2 + 2hx + h^2) - 4x - 4h + 3
= 2x^2 + 4hx + 2h^2 - 4x - 4h + 3
f(x+h)-f(x)
= 2x^2 + 4hx + 2h^2 - 4x - 4h + 3 - 2x^2 + 4x - 3
= 4hx + 2h^2 - 4h
notice all the "non-h" terms dropped out.
This MUST always happen.
If you find any terms without an "h", you made an error