1/2X ^ 2 +2 XY ^ 2 +2 Y ^ 4 = 1/2(x ^ 2 +4 XY ^ 2 +4 Y ^ 4) = 1/2(x +2 y 2)2
1/2x^2+2xy^2+2y^4=1/2(x^2+4xy^2+4y^4)=1/2(x+2y)²
=1/2(x^2+4xy^2+4y^4)=1/2(x+2y^2)^2