To simplify the expression \((2-m)(-m-2)-(5+m)^2\), let's break it down step by step.
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: \[ -2m - 4 + m^2 + 2m = m^2 - 4 \]
Expand \((5+m)^2\):
Using the formula \((a + b)^2 = a^2 + 2ab + b^2\): \[ (5+m)^2 = 5^2 + 2(5)(m) + m^2 = 25 + 10m + m^2 \]
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:
\[ \boxed{-10m - 29} \]