(2-m) (-m-2)-(5+m)²

To simplify the expression \((2-m)(-m-2)-(5+m)^2\), let's break it down step by step. 1. **Expand \((2-m)(-m-2)\)**: \[ (2-m)(-m-2) = 2(-m-2) - m(-m-2) \] Now calculate each term: \[ 2(-m-2) = -2m - 4 \] \[ -m(-m-2) = m^2 + 2m \] Combine these results: \[ -2m - 4 + m^2 + 2m = m^2 - 4 \] 2. **Expand \((5+m)^2\)**: Using the formula \((a + b)^2 = a^2 + 2ab + b^2\): \[ (5+m)^2 = 5^2 + 2(5)(m) + m^2 = 25 + 10m + m^2 \] 3. **Combine the two parts**: Now, take the result from step 1 and subtract the result from step 2: \[ (m^2 - 4) - (25 + 10m + m^2) \] Distributing the negative sign: \[ m^2 - 4 - 25 - 10m - m^2 = -4 - 25 - 10m \] Combine like terms: \[ -29 - 10m \] So, the final simplified expression is: \[ \boxed{-10m - 29} \]