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\frac{1024a^{2}-1}{16}
Factor out \frac{1}{16}.
\left(32a-1\right)\left(32a+1\right)
Consider 1024a^{2}-1. Rewrite 1024a^{2}-1 as \left(32a\right)^{2}-1^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
\frac{\left(32a-1\right)\left(32a+1\right)}{16}
Rewrite the complete factored expression.