Question

Factorise the following:

8a³ – b³ – 12a²b + 6ab²

Answer 1

8a³ – b³ − 12a²b + 6ab²

Rearrange terms to group them differently

= 8a³ − 12a²b + 6ab² – b³

= (8a³ – 12a²b) + (6ab² – b³)

= 4a²(2a – 3b) + b²(6a – b)

Now the issue here is the factors are not the same:

2a – 3b vs 6a – b

Alternate approach: Recognise sum/difference of cubes

8a³– b³ = (2a)³ – b³

= (2a − b)(4a² + 2ab + b²)

Use long division (polynomial division) to divide by (2a − b)

8a³ – b³ − 12a²b + 6ab² ÷ (2a − b)

= (2a – b)(4a² – 4ab + b²)