How do you know if #5y^4+10y^2+5# is a perfect square trinomial and how do you factor it?

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Answer 1 · 2015-06-07T20:36:10

It is a perfect square trinomial, it is of the form

#a^2+2ab+b^2 = (a+b)^2#, with #a=sqrt(5)y^2# and #b=sqrt(5)#.

So we can write:

#5y^4+10y^2+5 = (sqrt(5)y^2+sqrt(5))^2#

Generally it's nicer to use rational coefficients if possible and write instead:

#5y^4+10y^2+5 = 5(y^2+1)^2#

#(y^2+1)# has no simpler factors with real coefficients because:

#y^2+1 >= 1 > 0# for all #y in RR#