SOLUTION: How do you factor x^4 +x^2*y^2+y^4 into (x^2+xy+y^2)(x^2-xy+y^2)? Thank you.

We recognize that if there were a 2 coefficient on the
middle term, the expression with be a perfect square
trinomial.  We can make it have a coefficient of 2 by
adding .  But if we do that we'll have to also
subtract  to offset.

But that's OK for then we'll have the difference of 
two squares, and we know how to factor that.

So we add  to the middle term to make it 
 and then subtract :





factor the first term as a perfect square and write the
second term as a square



which is the difference of two squares, and factors
like  with  and :



Remove the inner parentheses:



Write in descending order of x and ascending order of y:



Edwin