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2\left(a^{2}+a^{2}b^{2}\right)
Factor out 2.
a^{2}\left(1+b^{2}\right)
Consider a^{2}+a^{2}b^{2}. Factor out a^{2}.
2a^{2}\left(1+b^{2}\right)
Rewrite the complete factored expression. Polynomial 1+b^{2} is not factored since it does not have any rational roots.