Question

Factorise:

`8x^3 − y^3/343`

Answer 1

Given, `8x^3 - y^3/343`

Factorise the given expression by using a suitable identity.

⇒ `8x^3 - y^3/343 = (2x)^3 - (y/7)^3`

By using identity,

a³ – b³ = (a – b) (a² + ab + b²)

`a = 2x` and `b = y/7`

= `(2x - y/7) (2x + 2x y/7 + (y/7)^2)`

= `(2x - y/7) (4x^2 + 2/7 xy + y^2/49)`

Therefore, `8x^3 - y^3/343 = (2x - y/7) (4x^2 + 2/7 xy + y^2/49)`