Find the product using suitable identities:

(i) (3a + 4b)(9a² - 12ab + 16b²)

(ii) $\Big(y - \dfrac{6}{y}\Big)\Big(y^2 + 6 + \dfrac{36}{y^2}\Big)$

(i) Given,

⇒ (3a + 4b)(9a² - 12ab + 16b²)

⇒ (3a + 4b)(3a)² + (4b)² - 3a × 4b

Using identity,

⇒ (a + b)(a² - ab + b²) = (a³ - b³)

⇒ (3a)³ + (4b)³

Hence, (3a + 4b)(9a² - 12ab + 16b²) = 27a³ + 64b³.

(ii) Using identity,

⇒ (a - b)(a² + ab + b²) = (a³ - b³)

Given,

$\Rightarrow \Big(y - \dfrac{6}{y}\Big)\Big(y^2 + 6 + \dfrac{36}{y^2}\Big) \\[1em] \Rightarrow \Big(y - \dfrac{6}{y}\Big)\Big(y^2 + y \times \dfrac{6}{y} + \Big(\dfrac{6}{y}\Big)^2\Big) \\[1em] \Rightarrow y^3 - \Big(\dfrac{6}{y}\Big)^3 \\[1em] \Rightarrow y^3 - \dfrac{216}{y^3}.$

Hence, $\Big(y - \dfrac{6}{y}\Big) \Big(y^2 + 6 + \dfrac{36}{y^2}\Big) = y^3 - \dfrac{216}{y^3}$.