Factorise : 3 - 5x + 5y - 12(x - y)^2 - Vidyadip

Question

Factorise : $3 - 5x + 5y - 12(x - y)^2$

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Answer

$3 - 5x + 5y - 12(x - y)^2= 3 - 5( x - y ) - 12(x - y)^2$
Let us assume that $x - y = a$
Then the given expression is
$3 - 5x + 5y - 12(x - y)^2$
$= 3 - 5a - 12a^2$
$= 3 - 9a + 4a - 12a^2$
$= 3( 1 - 3a ) + 4a( 1 - 3a )$
$= ( 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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