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