Question

Simplify:
(x + y - z)² + (x - y + z)²

Answer 1

(x + y - z)² + (x - y + z)²
= x² + y² + z² + 2(x)(y) + 2(y)(-z) + 2(x)(-z) + x² + y² + z² + 2(x)(-y) + 2(-y) + 2(x)(z)
= x² + y² + z² + 2xy - 2yz - 2xz + x² + y² + z² - 2xy - 2yz + 2xz
= 2x² + 2y² + 2z² - 4yz.