Question
Factorise : $a^2+ b^2- c^2- d^2+ 2ab - 2cd$
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Answer
$a^2+ b^2- c^2- d^2+ 2ab - 2cd$
$= ( a^2 + b^2 + 2ab ) - ( c^2 + d^2 + 2cd )$
$= ( a + b )^2 - ( c + d )^2$
$= [( a + b ) - ( c + d )][( a + b ) + ( c + d )] [\because a^2 - b^2 = ( a + b )( a - b )]$
$= ( a + b - c - d )( a + b + c + d )$
$= ( a^2 + b^2 + 2ab ) - ( c^2 + d^2 + 2cd )$
$= ( a + b )^2 - ( c + d )^2$
$= [( a + b ) - ( c + d )][( a + b ) + ( c + d )] [\because a^2 - b^2 = ( a + b )( a - b )]$
$= ( a + b - c - d )( a + b + c + d )$
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