#### (i) (2p + 3q) (4p^{2} – 6pq + 9q^{2})

#### (ii) (x + 1/x) (x^{2} – 1 + 1/x^{2})

**Answer :**

**(i) (2p + 3q) (4p**^{2} – 6pq + 9q^{2})

^{2}– 6pq + 9q

^{2})

It can be written as

= (2p + 3q) [(2p)^{2} – 2p × 3q + (3q)^{2}]

By further simplification

= (2p)^{3} + (3q)^{3}

= 8p^{3} + 27q^{3}

**(ii) (x + 1/x) (x**^{2} – 1 + 1/x^{2})

^{2}– 1 + 1/x

^{2})

It can be written as

= (x + 1/x) [x^{2} – x × 1/x + (1/x)^{2}]

By further simplification

= x^{3} + (1/x)^{3}

= x^{3} + 1/x^{3}