Polynomial and Function I have been give a question if 
  $ f(x) = x^3-1 $
then show 
$$  \frac {f(b) - f(a)} {b-a} =b^2+ab+a^2 $$ 
how to show that the above fraction is equal to that polynomial if $ f(X) = x^3-1 $ ?

$$  \frac {f(b) - f(a)} {b-a}$$
$$ = \frac {b^3 - 1 - a^3 + 1} {b-a}$$
$$ = \frac {b^3 - a^3} {b-a}$$
$$ = \frac {(b-a)(b^2+ab+a^2)} {b-a} $$
$$ = b^2 + ab + a^2 $$
Formula used.
$$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$$
