1. **State the problem:** Simplify or factor the expression $A^3 - A^2 - 8A + 8$. 2. **Recall the factoring formula:** For cubic polynomials, try factoring by grouping or use the factor theorem. 3. **Group terms:** $(A^3 - A^2) - (8A - 8)$. 4. **Factor each group:** $A^2(A - 1) - 8(A - 1)$. 5. **Factor out the common binomial:** $(A - 1)(A^2 - 8)$. 6. **Recognize difference of squares:** $A^2 - 8 = A^2 - (2\sqrt{2})^2$. 7. **Factor difference of squares:** $(A - 1)(A - 2\sqrt{2})(A + 2\sqrt{2})$. **Final answer:** $$A^3 - A^2 - 8A + 8 = (A - 1)(A - 2\sqrt{2})(A + 2\sqrt{2})$$