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

If p = 4, q = -3 and r = 2, find the value of: p³ + q³ - r³ - 3pqr

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

State which of the following are equations with a variable. In case of an equation with a variable, identify the variable.

(i) 17 + x = 5

(ii) 2b − 3 = 7

(iii) (y - 7) > 5

(iv) $\dfrac{9}{3} = 3$

(v) 7 × 3 − 19 = 2

(vi) 5 × 4 − 8 = 3t

(vii) 2p < 15

(viii) 7 = 11 × 5 − 12 × 4

(ix) $\dfrac{3}{2}q = 5$