a)
(x+y)² + (x-y)²
= x² + 2xy + y² + x² - 2xy +y²
= 2x² + 2y²
b)
2(x-y)(x+y) + (x-y)² + (x+y)²
= 2(x² - y²) + x² - 2xy + y² + x² + 2xy + y²
= 2x² - 2y² + x² - 2xy + y² + x² + 2xy + y²
= x²(2 + 1 + 1) + y²(1 + 1 - 2) + xy (2 - 2)
= 4x²
c)
(x - y + z)² + (z - y)² + 2(x - y + z)(y - z)
= x² + y² + z² + 2xz - 2xy - 2yz + z² - 2yz + y² + 2(xy - xz - y² + yz - z²)
= x² + 2y² + 2z² + 2xz - 2xy - 4yz + 2xy - 2xz - 2y² + 2yz - 2z²
= x² - 2yz
