Using standard formulae, expand each of the following:

(i) (2 - x)(2 + x)(4 + x²)

(ii) (x + y)(x - y)(x² + y²)

We know that,

(a + b)(a - b) = a² - b²

(i) Given,

⇒ (2 - x)(2 + x)(4 + x²)

⇒ [(2)² - (x)²](4 + x²)

⇒ (4 - x²)(4 + x²)

⇒ (4)² - (x²)²

⇒ 16 - x⁴.

Hence, (2 - x)(2 + x)(4 + x²) = 16 - x⁴.

(ii) Given,

⇒ (x + y)(x - y)(x² + y²)

⇒ [(x)² - (y)²](x² + y²)

⇒ (x² - y²)(x² + y²)

⇒ (x²)² - (y²)²

⇒ (x⁴ - y⁴).

Hence, (x + y)(x - y)(x² + y²) = (x⁴ - y⁴).