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2\left(ax^{2}-4ay^{2}\right)
Factor out 2.
a\left(x^{2}-4y^{2}\right)
Consider ax^{2}-4ay^{2}. Factor out a.
\left(x-2y\right)\left(x+2y\right)
Consider x^{2}-4y^{2}. Rewrite x^{2}-4y^{2} as x^{2}-\left(2y\right)^{2}. The difference of squares can be factored using the rule: p^{2}-q^{2}=\left(p-q\right)\left(p+q\right).
2a\left(x-2y\right)\left(x+2y\right)
Rewrite the complete factored expression.