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