Using standard formulae, expand each of the following:

(i) (3a + 2b)(3a - 2b)

(ii) $\Big(5x + \dfrac{1}{5x}\Big)\Big(5x - \dfrac{1}{5x}\Big)$

(iii) $\Big(2x^2 + \dfrac{3}{x^2}\Big)\Big(2x^2 - \dfrac{3}{x^2}\Big)$

Using standard formulae, expand each of the following:

(i) (2 - x)(2 + x)(4 + x²)

(ii) (x + y)(x - y)(x² + y²)

Simplify:

(i) (a + b)² + (a - b)²

(ii) (a + b)² - (a - b)²

(iii) $\Big(x + \dfrac{1}{x}\Big)^2 + \Big(x - \dfrac{1}{x}\Big)^2$

(iv) $\Big(x + \dfrac{1}{x}\Big)^2 - \Big(x - \dfrac{1}{x}\Big)^2$

(v) $\Big(\dfrac{a}{2b} + \dfrac{2b}{a}\Big)^2 - \Big(\dfrac{2b}{a} - \dfrac{a}{2b}\Big)^2$

(vi) $\Big(3x - \dfrac{1}{3x}\Big)^2 - \Big(3x + \dfrac{1}{3x}\Big)\Big(3x - \dfrac{1}{3x}\Big)$

(vii) (5a + 3b)² - (5a - 3b)² - 60ab

(viii) (3x + 1)² - (3x + 2)(3x - 1)

(i) If (a + b) = 7 and ab = 10, find the value of (a - b).

(ii) If (x - y) = 5 and xy = 24, find the value of (x + y).