1. **State the problem:** Simplify the expression $x^2y^2 - 5x^2y - 5xy^2 + xy^3$. 2. **Identify common factors:** Group terms to factor by grouping: $$ (x^2y^2 - 5x^2y) + (-5xy^2 + xy^3) $$ 3. **Factor each group:** - From the first group, factor out $x^2y$: $$ x^2y(y - 5) $$ - From the second group, factor out $xy^2$: $$ xy^2(-5 + y) $$ 4. **Rewrite the second group:** Note that $-5 + y = y - 5$, so: $$ xy^2(y - 5) $$ 5. **Factor out the common binomial $(y - 5)$:** $$ (y - 5)(x^2y + xy^2) $$ 6. **Factor out common factors in the second parenthesis:** $$ (y - 5)(xy(x + y)) $$ 7. **Final simplified form:** $$ xy(y - 5)(x + y) $$ This is the fully factored form of the original expression.