` A = (x - y)² + (x + y)² `

= $x^{2}$ - ` 2xy + ` $y^{2}$ + $x^{2}$  + ` 2xy + ` $y^{2}$

= ` (x² + x²) + (2xy - 2xy) + (y² + y²) `

= ` 2x² + 2y² `