..16 - 4x^4 - 4y^2 - 8x^2y

= (-4x^4 - 4y^2 - 8x^2y) + 16

= -4(x^4 + y^2 + 2x^2y) + 16

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

= 4^2 - [4(x^4 + y^2 + 2x^2y)]

Mr F chips in:

where and

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

using the difference of two squares formula.

What I don't understand is the transition from4^2 - [2(x+y)]^2to4(2 + x^2 + y)(2 - x^2 - y)

If someone could explain it, that would be great thanks.