1. **State the problem:** Simplify the expression $100m - 15(2m+1)(m+1)$. 2. **Recall the distributive property and multiplication of binomials:** To simplify, first expand the product $(2m+1)(m+1)$ using the FOIL method: $$ (2m+1)(m+1) = 2m \cdot m + 2m \cdot 1 + 1 \cdot m + 1 \cdot 1 = 2m^2 + 2m + m + 1 = 2m^2 + 3m + 1 $$ 3. **Substitute back into the expression:** $$ 100m - 15(2m^2 + 3m + 1) $$ 4. **Distribute the $-15$ across the trinomial:** $$ 100m - 15 \cdot 2m^2 - 15 \cdot 3m - 15 \cdot 1 = 100m - 30m^2 - 45m - 15 $$ 5. **Combine like terms:** $$ 100m - 45m = 55m $$ So the expression becomes: $$ -30m^2 + 55m - 15 $$ 6. **Final simplified expression:** $$ \boxed{-30m^2 + 55m - 15} $$