1. **State the problem:** Factor the expression $$x^2y^2 - 5x^2y - 5xy^2 + xy^3$$. 2. **Recall the factoring technique:** Group terms to factor by grouping. 3. **Group the terms:** $$ (x^2y^2 - 5x^2y) - (5xy^2 - xy^3) $$ 4. **Factor out common factors in each group:** $$ x^2y(y - 5) - xy^2(5 - y) $$ 5. **Rewrite the second group to match the first factor:** Since $$5 - y = -(y - 5)$$, we have $$ x^2y(y - 5) + xy^2(y - 5) $$ 6. **Factor out the common binomial:** $$ (y - 5)(x^2y + xy^2) $$ 7. **Factor further if possible:** Factor out $$xy$$ from the second factor: $$ (y - 5)xy(x + y) $$ **Final factored form:** $$ (y - 5)xy(x + y) $$