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\frac{4b^{2}-12ab^{2}+9a^{2}b^{2}}{9}
Factor out \frac{1}{9}.
b^{2}\left(4-12a+9a^{2}\right)
Consider 4b^{2}-12ab^{2}+9a^{2}b^{2}. Factor out b^{2}.
\left(3a-2\right)^{2}
Consider 4-12a+9a^{2}. Use the perfect square formula, p^{2}-2pq+q^{2}=\left(p-q\right)^{2}, where p=3a and q=2.
\frac{b^{2}\left(3a-2\right)^{2}}{9}
Rewrite the complete factored expression.