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3\left(z^{2}-9\right)
Factor out 3.
\left(z-3\right)\left(z+3\right)
Consider z^{2}-9. Rewrite z^{2}-9 as z^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
3\left(z-3\right)\left(z+3\right)
Rewrite the complete factored expression.