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Question
Factorise : a2 + b2 - c2 - d2 + 2ab - 2cd
Solution
a2 + b2 - c2 - d2 + 2ab - 2cd
= ( a2 + b2 + 2ab ) - ( c2 + d2 + 2cd )
= ( a + b )2 - ( c + d )2
= [( a + b ) - ( c + d )][( a + b ) + ( c + d )] [∵ a2 - b2 = ( a + b )( a - b )]
= ( a + b - c - d )( a + b + c + d )
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