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3\left(axy^{2}-9ax\right)
Factor out 3.
ax\left(y^{2}-9\right)
Consider axy^{2}-9ax. Factor out ax.
\left(y-3\right)\left(y+3\right)
Consider y^{2}-9. Rewrite y^{2}-9 as y^{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).
3ax\left(y-3\right)\left(y+3\right)
Rewrite the complete factored expression.