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\frac{4a^{3}-4a^{2}+a}{4}
Factor out \frac{1}{4}.
a\left(4a^{2}-4a+1\right)
Consider 4a^{3}-4a^{2}+a. Factor out a.
\left(2a-1\right)^{2}
Consider 4a^{2}-4a+1. Use the perfect square formula, p^{2}-2pq+q^{2}=\left(p-q\right)^{2}, where p=2a and q=1.
\frac{a\left(2a-1\right)^{2}}{4}
Rewrite the complete factored expression.