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how can I factorize $4a^3b-9ab$ ?

it's not in the shape of any common factorization formula like $(a+b)^2=a^2+b^2+2ab$ or ...

so it must be factorized indirectly (maybe by adding and subtracting some monomials).

anyhow I don't have any idea to do it. who can help?

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    $\begingroup$ Notice that $4a^3b=4a^2ab$ $\endgroup$ – Claude Leibovici Feb 13 '15 at 7:44
  • $\begingroup$ First factor out $ab$. $\endgroup$ – Alp Uzman Feb 13 '15 at 7:46
  • $\begingroup$ yes @Uzman. got it. $\endgroup$ – AHB Feb 13 '15 at 7:51
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$$4a^3b-9ab=a(4a^2b-9b)=ab(4a^2-9)=ab(2a+3)(2a-3)$$

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