Question

The factors of 8a³ + b³ − 6ab + 1 are

Options

• (2a + b − 1) (4a² + b² + 1 − 3ab − 2a)

•  (2a − b + 1) (4a² + b² − 4ab + 1 − 2a + b)

• (2a + b + 1) (4a² + b² + 1 −2ab − b − 2a)

• (2a − 1 + b) (4a² + 1 − 4a − b − 2ab)

Answer 1

The given expression to be factorized is  8a³ + b³ − 6ab + 1

This can be written in the form

8a³ + b³ − 6ab + 1 = 8a³ + b³ +1 − 6ab 

` = (2a)^3 + (b)^3 + (1)^3 -3.(2a).(b).(1)`

Recall the formula

`a^3 +b^3 + c^3 -3abc = (a+b +c) (a^2 +b^2 + c^2 - ab - bc -ca)`

Using the above formula, we have 

 8a³ + b³ − 6ab + 1

`= (2a +b +1){(2a)^2 + (b)^2 +(1)^2 - (2a).(b) - (b).(1) - (1).(2a)}`

` = (2a +b +1)(4a^2 + b^2 + 1 - 2ab - b -2a)`