SOLUTION: Factor a) a^4 +a^2b^2 +b^4 b) a^4 +4b^4

Question 1139340: Factor
a) a^4 +a^2b^2 +b^4
b) a^4 +4b^4
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.


a)  a^4 +a^2b^2 +b^4 = 


           add and subtract  a^2*b^2


    = (a^4 + 2a^2*b^2 + b^4) - a^2*b^2  =  -  = 


          apply the formula   -  = (x+y)*(x-y)


    = .     ANSWER

Done; i.e. factored.

b)  a^4 + 4b^4 = a^4 + (2b^2)^2 = 


           add and subtract  2*a^2*(2b^2)


    = (a^4 + 2*a^2*(2b^2) + 4b^4) - 2*a^2*(2b^2) = 


    = (a^2 + 2b^2)^2 - 4*a^2*b^2 = 


    = (a^2 + 2b^2)^2 - (2ab)^2 = 


          apply the formula   -  = (x+y)*(x-y)


   = (a^2 - 2ab + 2b^2)*(a^2 + 2ab + 2b^2).

Done; i.e. factored.

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See the lesson
- Advanced factoring
in this site.

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