Question

where did that underlined x go.

Answer 1

they completed the square by both adding and subtracting 2x^2y^2.

x^4 + x^2y^2 + y^4

(x^4 + 2x^2y^2 +y^4) - 2x^2y^2 + x^2y^2
(x^2 + y^2)^2 - 2x^2y^2 + x^2y^2