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Question
Factorize the following expressions:
8a3 - b3 - 4ax + 2bx
Solution
= 8a3 - b3 - 2x (2a - b)
= (2a )3 - b3 - 2x (2a - b)
= (2a - b)((2a)2 + 2a ´ b + b2 )- 2x (2a - b) [∵ a3 - b3 = (a - b)(a2 + ab + b2 )]
= (2a - b)(4a2 + 2ab + b2 ) - 2x (2a - b)
= (2a - b)(4a2 + 2ab + b2 - 2x)
∴ 8a3 - b3 - 4ax + 2bx = (2a - b)(4a2 + 2ab + b2 - 2x)
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