1. **State the problem:** Simplify or factor the expression $$a^3 - a^2b + 4a - 4b$$. 2. **Identify the formula or method:** We will try to factor by grouping, which involves grouping terms to find common factors. 3. **Group terms:** Group the first two terms and the last two terms: $$a^3 - a^2b + 4a - 4b = (a^3 - a^2b) + (4a - 4b)$$ 4. **Factor out common factors in each group:** $$a^2(a - b) + 4(a - b)$$ 5. **Factor out the common binomial factor:** $$\cancel{(a - b)}(a^2 + 4)$$ 6. **Final factored form:** $$ (a - b)(a^2 + 4) $$ This is the simplified factored form of the expression. **Explanation:** We used factoring by grouping to find common factors in pairs of terms, then factored out the common binomial factor to simplify the expression.