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$4 \exponential{m}{2} - 2 m - \exponential{(2 m - 1)}{2} $
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4m^{2}-2m-\left(4m^{2}-4m+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-1\right)^{2}.
4m^{2}-2m-4m^{2}+4m-1
To find the opposite of 4m^{2}-4m+1, find the opposite of each term.
-2m+4m-1
Combine 4m^{2} and -4m^{2} to get 0.
2m-1
Combine -2m and 4m to get 2m.
4m^{2}-2m-\left(4m^{2}-4m+1\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2m-1\right)^{2}.
4m^{2}-2m-4m^{2}+4m-1
To find the opposite of 4m^{2}-4m+1, find the opposite of each term.
-2m+4m-1
Combine 4m^{2} and -4m^{2} to get 0.
2m-1
Combine -2m and 4m to get 2m.