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