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Question
Factorise : 4(2x - 3y)2 - 8x+12y - 3
Solution
4(2x - 3y)2 - 8x+12y - 3
= 4(2x - 3y)2 - 4(2x - 3y) - 3
Let us assume that 2x - 3y = a
Then the given expression is
4(2x - 3y)2 - 8x+12y - 3
= 4a2 - 4a - 3
= 4a2 - 6a + 2a - 3
= 2a( 2a - 3 ) + 1( 2a - 3)
= ( 2a - 3 )( 2a + 1 )
= [ 2( 2x - 3y ) - 3 ][ 2( 2x - 3y ) + 1 ]
= ( 4x - 6y - 3 )( 4x - 6y + 1 )
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