Simplify $(a-1)(a+1)(a+2) - (a-2)(a+1).$
(a - 1) ( a + 1) ( a + 2) - (a - 2) (a + 1) =
(a + 1) [ (a - 1) ( a + 2) - (a - 2)] =
(a + 1) [ [ a^2 + a - 2 - a + 2 ] =
(a + 1) [ a^2 ] =
a^3 + a^2
