# How to solve this polynomial problem

$(3x-1)^4=a_4x^4+a_3x^3+a_2x^2+a_1x+a_0$

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.

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

HINT: try putting $x=\frac 13$
Hint: using Pascal's triangle/the binomial theorem you can easily expand $(3x-1)^4$ and determine $a_0,\dots,a_4$.