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\frac{16x^{2}+8x+1}{16}
Factor out \frac{1}{16}.
\left(4x+1\right)^{2}
Consider 16x^{2}+8x+1. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=4x and b=1.
\frac{\left(4x+1\right)^{2}}{16}
Rewrite the complete factored expression.