The fourth power of x plus the fourth power of y plus the fourth power of the sum of x and y.

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

=(X^2+Y^2)^2-2(XY)^2+(X+Y)^4

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

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

Let (x+y) 2 = z: = [z-2xy] 2-2 (xy) 2+z 2.

=Z^2-4ZXY+4(XY)^2-2(XY)^2+Z^2

=2Z^2-4ZXY+2(XY)^2

=2[Z^2-2ZXY+(XY)^2]

=2(Z-XY)^2

=2[(X+Y)^2-XY]^2

=2(X^2+Y^2+XY)^2

In fact, such a topic is very simple. He has only one principle, which can be easily achieved as long as you grasp it.