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

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

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).