#### (i) (3x + 1/x)^{3}

#### (ii) (2x – 1)^{3}

**Answer :**

**(i) (3x + 1/x)**^{3}

^{3}

It can be written as

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

By further calculation

= 27x^{3} + 1/x^{3} + 9 (3x + 1/x)

So we get

= 27x^{3} + 1/x^{3} + 27x + 9/x

**(ii) (2x – 1)**^{3}

^{3}

It can be written as

= (2x)^{3} – 1^{3} – 3 × 2x × 1 (2x – 1)

By further calculation

= 8x^{3} – 1 – 6x (2x – 1)

So we get

= 8x^{3} – 1 – 12x^{2} + 6x

= 8x^{3} – 12x^{2} + 6x – 1

**More Solutions:**

- Simplify the following (a + b)2 + (a – b)2
- Simplify the following (a + 1/a)2 + (a – 1/a)2
- Simplify the following (3x – 1)2 – (3x – 2) (3x + 1)
- Simplify the following (7p + 9q) (7p – 9q)
- Simplify the following (2x – y + 3) (2x – y – 3)
- Simplify the following (x + 2/x – 3) (x – 2/x – 3)
- Simplify the following (x + 2y + 3) (x + 2y + 7)
- Simplify the following (2p + 3q) (4p2 – 6pq + 9q2)
- Simplify the following (3p – 4q) (9p2 + 12pq + 16q2)
- Simplify the following (2x + 3y + 4z)