SOLUTION: Factor completely. Show work y^4 - 8y^2 – 9 i am lost

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Factor completely. Show work y^4 - 8y^2 – 9 i am lost      Log On


   

Question 300764: Factor completely. Show work
y^4 - 8y^2 – 9
i am lost
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Make a substitution.
Let u=y%5E2, then u%5E2=y%5E4
+y%5E4-8y%5E2-9+=u%5E2-8u-9
y%5E4-8y%5E2-9=%28u%2B1%29%28u-9%29
Now substitute back,
y%5E4-8y%5E2-9=%28y%5E2%2B1%29%28y%5E2-9%29
Both can be factored as a difference of two squares,
y%5E4-8y%5E2-9=%28y%2Bi%29%28y-i%29%28y-3%29%28y%2B3%29 where i=sqrt%28-1%29