prove that x^3 = x for x=0,1,-1 but not by just putting in the values of x??
$\displaystyle x^3 = x$
$\displaystyle x^3 - x = 0$
$\displaystyle x(x^2 - 1) = 0$
$\displaystyle x(x - 1)(x + 1) = 0$
$\displaystyle x = 0$ or $\displaystyle x-1=0$ or $\displaystyle x+1 = 0$
$\displaystyle x = 0$ or $\displaystyle x=1$ or $\displaystyle x=-1$.