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Question
Factorise : 3 - 5x + 5y - 12(x - y)2
Solution
3 - 5x + 5y - 12(x - y)2 = 3 - 5( x - y ) - 12(x - y)2
Let us assume that x - y = a
Then the given expression is
3 - 5x + 5y - 12(x - y)2
= 3 - 5a - 12a2
= 3 - 9a + 4a - 12a2
= 3( 1 - 3a ) + 4a( 1 - 3a )
= ( 3 + 4a )( 1 - 3a ) [ resubstitute the value of a ]
= [ 3 + 4( x - y )][ 1 - 3( x - y )]
= ( 3 + 4x - 4y )( 1 - 3x + 3y )
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