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\frac{a^{2}-8ab-4ac+16b^{2}+16bc+4c^{2}}{4}
Factor out \frac{1}{4}.
\left(a-4b-2c\right)^{2}
Consider a^{2}-8ab-4ac+16b^{2}+16bc+4c^{2}. Use the perfect square formula, p^{2}+q^{2}+r^{2}+2pq+2pr+2qr=\left(p+q+r\right)^{2}, where p=a, q=-4b and r=-2c.
\frac{\left(a-4b-2c\right)^{2}}{4}
Rewrite the complete factored expression.