Value required to be found :- $a_4+3a_3+9a_2+27a_1+81a_0$

I can find the value of $a_4+a_3+a_2+a_1+a_0$.Then I don't know how to continue.Please help.

  • $\begingroup$ Can't you just expand it? $\endgroup$ Aug 20, 2015 at 9:21
  • $\begingroup$ @principal-ideal-domain-Method looks dull...:-) $\endgroup$
    – Soham
    Aug 20, 2015 at 9:22
  • $\begingroup$ Sure, but I guess you would be faster by doing so than typing the question here. $\endgroup$ Aug 20, 2015 at 9:24

2 Answers 2


HINT: try putting $x=\frac 13$

  • $\begingroup$ Nice @davidquinn. Your answers are always very intuitive and simple. $\endgroup$
    – Shailesh
    Aug 20, 2015 at 10:53
  • $\begingroup$ @Shailesh thanks very much! The length of my answers is usually in proportion to my skill and patience with Mathjax $\endgroup$ Aug 20, 2015 at 11:53

Hint: using Pascal's triangle/the binomial theorem you can easily expand $(3x-1)^4$ and determine $a_0,\dots,a_4$.


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