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