Question

Factorise 8b^3- 1/27​

Answer 1

Answer :-

(2b - 1/3)(4b² + 2b/3 + 1/9)

Solution :-

8b³ - 1/27

It can be written as

= (2b)³ - 1/3³

= (2b)³ - 1³/3³

= (2b)³ - (1/3)³

We know that

x³ - y³ = (x - y)(x² + xy + y²)

Here

• x = 2b

• y = 1/3

By substituting the values

= (2b - 1/3){(2b)² + 2b(1/3) + (1/3)²}

= (2b - 1/3)(4b² + 2b/3 + 1²/3²)

= (2b - 1/3)(4b² + 2b/3 + 1/9)

Identity used :-

• x³ - y³ = (x - y)(x² + xy + y²)