1. Stating the problem: Simplify the expression $x^2y^2 - 5x^2y - 5xy^2 + xy$. 2. Group terms to factor by grouping: $$x^2y^2 - 5x^2y - 5xy^2 + xy = (x^2y^2 - 5x^2y) + (-5xy^2 + xy)$$ 3. Factor out common factors in each group: $$x^2y(y - 5) - xy(5y - 1)$$ 4. Notice that $5y - 1$ is not the same as $y - 5$, so rewrite the second term: $$-xy(5y - 1) = -xy(5y - 1)$$ 5. Since the binomials are not the same, try factoring $xy$ from the entire expression: $$xy(xy - 5x - 5y + 1)$$ 6. The expression inside the parentheses is: $$xy - 5x - 5y + 1$$ 7. Try to factor this quadratic-like expression by grouping: Group as $(xy - 5x) + (-5y + 1)$ 8. Factor $x$ from the first group and $-1$ from the second: $$x(y - 5) - 1(5y - 1)$$ 9. Since $y - 5$ and $5y - 1$ are different, no further simple factorization is possible. Final simplified form is: $$xy(xy - 5x - 5y + 1)$$