Answer:
\[3{{a}^{2}}{{b}^{3}}-27{{a}^{4}}b=3{{a}^{2}}b({{b}^{2}}-9{{a}^{2}})\] \[=3{{a}^{2}}b\,[{{(b)}^{2}}-{{(3a)}^{2}}]\] \[=3{{a}^{2}}b(b+3a)(b-3a)\]
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