1. **State the problem:** Simplify the expression $$A = (x+2)(x^2 - x - 1) + (x-1)(x+2)$$. 2. **Recall the distributive property:** To simplify, we will expand each product using the distributive property (also called FOIL for binomials). 3. **Expand the first product:** $$ (x+2)(x^2 - x - 1) = x(x^2 - x - 1) + 2(x^2 - x - 1) $$ $$ = x^3 - x^2 - x + 2x^2 - 2x - 2 $$ $$ = x^3 + (-x^2 + 2x^2) + (-x - 2x) - 2 $$ $$ = x^3 + x^2 - 3x - 2 $$ 4. **Expand the second product:** $$ (x-1)(x+2) = x(x+2) - 1(x+2) $$ $$ = x^2 + 2x - x - 2 $$ $$ = x^2 + (2x - x) - 2 $$ $$ = x^2 + x - 2 $$ 5. **Add the two expanded expressions:** $$ A = (x^3 + x^2 - 3x - 2) + (x^2 + x - 2) $$ $$ = x^3 + (x^2 + x^2) + (-3x + x) + (-2 - 2) $$ $$ = x^3 + 2x^2 - 2x - 4 $$ 6. **Final simplified expression:** $$ \boxed{x^3 + 2x^2 - 2x - 4} $$ This is the simplified form of the given expression.