1. **State the problem:** Simplify the expression $$(m + 5n)(m - 2n) + 6n^2$$. 2. **Use the distributive property (FOIL) to expand:** $$ (m + 5n)(m - 2n) = m \cdot m + m \cdot (-2n) + 5n \cdot m + 5n \cdot (-2n) $$ 3. **Calculate each term:** $$ m^2 - 2mn + 5mn - 10n^2 $$ 4. **Combine like terms:** $$ m^2 + ( -2mn + 5mn ) - 10n^2 = m^2 + 3mn - 10n^2 $$ 5. **Add the remaining term $6n^2$:** $$ m^2 + 3mn - 10n^2 + 6n^2 = m^2 + 3mn - 4n^2 $$ 6. **Final simplified expression:** $$ \boxed{m^2 + 3mn - 4n^2} $$ This expression represents the combined area of the four smaller rectangles in the given figure, confirming the algebraic expansion matches the geometric interpretation.