Question

If f(x)= x(x+1), show that f(x +h)- f(x) = h(2x+1+h).

Answer 1

$f(x + h) - f(x) = (x + h)(x + h + 1) - x(x + 1) = {x^2} + hx + hx + {h^2} + x + h - {x^2} - x = 2hx + {h^2} + h = h(2x + h + 1)$

Q.E.D.