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\frac{x^{2}-12xy^{2}+36y^{4}}{4}
Factor out \frac{1}{4}.
\left(x-6y^{2}\right)^{2}
Consider x^{2}-12xy^{2}+36y^{4}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=x and b=6y^{2}.
\frac{\left(x-6y^{2}\right)^{2}}{4}
Rewrite the complete factored expression.