If a = 2, b = 3 and c = 1, find the value of: a² + b² + c² - 2ab - 2bc - 2ca + 3abc

If m = 1, n = 2 and p = 3, find the value of: 2mn⁴ - 15m²n - p

For x = 5 and y = 2, verify the following:

(i) (x + y)² = x² + 2xy + y²

(ii) (x - y)² = x² - 2xy + y²

(iii) x² - y² = (x + y)(x - y)

(iv) (x + y)² = (x - y)² + 4xy

(v) (x + y)³ = x³ + y³ + 3x²y + 3xy²