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Question
Factorise the following:
8a3 – b3 – 12a2b + 6ab2
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Solution
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)
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