(a + 3) (a - 3) (a+ 9)
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Step-by-step explanation:
a(a2+3a+9)=1 , so a2+3a+9=1/a. Thus, 3a=3a2+9a+27. So we have that a3+3a=a3+3a2+9a+27. However, by the original equation we have that a3+3a2+9a=1, so a3+3a2+9a+27=28, and we are done.
Motivation: The a3+3/a does not look very nice, so you want to isolate the 3/a somehow. This is a common technique in contests
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