SOLUTION: The problem is: factor completely; (x^4)-5(x^2)(y^2)+(4y^4) Any help is greatly appreciated!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The problem is: factor completely; (x^4)-5(x^2)(y^2)+(4y^4) Any help is greatly appreciated!      Log On


   

Question 834668: The problem is: factor completely; (x^4)-5(x^2)(y^2)+(4y^4)
Any help is greatly appreciated!
Found 2 solutions by Fombitz, LinnW:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution,
u=x%5E2
u%5E2=x%5E4
v=y%5E2
v%5E2=y%5E4
%28x%5E4%29-5%28x%5E2%29%28y%5E2%29%2B%284y%5E4%29=u%5E2-5uv%2B4v%5E2
%28x%5E4%29-5%28x%5E2%29%28y%5E2%29%2B%284y%5E4%29=%28u-4v%29%28u-v%29
%28x%5E4%29-5%28x%5E2%29%28y%5E2%29%2B%284y%5E4%29=%28x%5E2-4y%5E2%29%28x%5E2-y%5E2%29

Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E4%29-5%28x%5E2%29%28y%5E2%29%2B%284y%5E4%29
Let a = x^2
b = y^2
and the equation becomes
%28a%5E2%29-5%28a%29%28b%29%2B%284b%5E2%29
or
a%5E2-5ab%2B4b%5E2
now factor
%28a+-+1%29%28a+-+4%29
substituting back
%28x%5E2+-+1%29%28y%5E2+-+4%29
Now we need to factor further
%28x+%2B+1%29%28x+-+1%29%28y+%2B+2%29%28+y+-+2+%29