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\left(1-a\right)\left(1+a\right)
Rewrite -a^{2}+1 as 1^{2}-a^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
\left(-a+1\right)\left(a+1\right)
Reorder the terms.