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-a^{2}+\frac{1}{2}
Combine a^{2} and -2a^{2} to get -a^{2}.
\frac{2a^{2}-4a^{2}+1}{2}
Factor out \frac{1}{2}. Polynomial -2a^{2}+1 is not factored since it does not have any rational roots.