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Question
Factorise : (a + b)3 - a - b
Sum
Solution
(a + b)3 - a - b
= ( a + b )3 - ( a + b )
= ( a + b )[ ( a + b )2 - 1 ]
= ( a + b )[ ( a + b )2 - (1)2 ]
= ( a + b )[( a + b ) + 1 ][( a + b ) - 1] [ ∵ a2 - b2 = ( a + b )( a - b )]
= ( a + b )( a + b + 1 )( a + b - 1 )
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Method of Factorisation : Difference of Two Squares
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