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