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\frac{ax^{3}-9ax}{9}
Factor out \frac{1}{9}.
ax\left(x^{2}-9\right)
Consider ax^{3}-9ax. Factor out ax.
\left(x-3\right)\left(x+3\right)
Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
\frac{ax\left(x-3\right)\left(x+3\right)}{9}
Rewrite the complete factored expression.