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\sqrt{3}\left(a^{2}-1\right)
Factor out \sqrt{3}.
\left(a-1\right)\left(a+1\right)
Consider a^{2}-1. Rewrite a^{2}-1 as a^{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).
\sqrt{3}\left(a-1\right)\left(a+1\right)
Rewrite the complete factored expression.