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\frac{2x^{2}\log_{e}\left(x\right)-\left(2a+1\right)x^{2}+8x}{4}
Factor out \frac{1}{4}.
x\left(2x\log_{e}\left(x\right)-\left(2a+1\right)x+8\right)
Consider 2x^{2}\ln(x)\times \frac{1}{\ln(e)}-\left(2a+1\right)x^{2}+8x. Factor out x.
\frac{x\left(2x\log_{e}\left(x\right)-\left(2a+1\right)x+8\right)}{4}
Rewrite the complete factored expression.