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