​ Simplify each of the following expressions: (i) (x+y+z)^2+ (x+y/2+z/3)^2 - (x/2+y/3+z/4)^2 (ii) (x+y - 2z)^2 - x^2 – y^2 - 3z^2+4xy

Question

Simplify each of the following expressions:

(i) (x+y+z)²+ \((x-\frac{y}{2}+\frac{z}{3})^2\) - \((\frac{x}{2}-\frac{y}{3}+\frac{z}{4})^2\)

(ii) (x+y-2z)²-x² – y² - 3z²+4xy

(iii) (x² – x + 1)² - (x² + x + 1)²

Answer 1

(i) Using identity,

(ii) Using the identity,

(iii) Using the identity