Question

Factorise : 3 - 5x + 5y - 12(x - y)²

Answer 1

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 )