Question
Factorise : $4x^2- 12ax - y^2- z^2- 2yz + 9a^2$
✓
Answer
$4x^2- 12ax - y^2- z^2- 2yz + 9a^2$
$= 4x^2 + 9a^2 - 12ax - y^2 - z^2 - 2yz$
$= ( 2x )^2 + ( 3a )^2 - 12ax - ( y^2 + z^2 + 2yz )$
$= ( 2x - 3a )^2 - ( y + z )^2$
$= [( 2x - 3a ) - ( y + z )][( 2x - 3a ) + ( y + z )]$
$[ \because a^2 - b^2 = ( a + b )( a - b )]$
$= [ 2x - 3a - y - z ][ 2x - 3a + y + z ]$
$= 4x^2 + 9a^2 - 12ax - y^2 - z^2 - 2yz$
$= ( 2x )^2 + ( 3a )^2 - 12ax - ( y^2 + z^2 + 2yz )$
$= ( 2x - 3a )^2 - ( y + z )^2$
$= [( 2x - 3a ) - ( y + z )][( 2x - 3a ) + ( y + z )]$
$[ \because a^2 - b^2 = ( a + b )( a - b )]$
$= [ 2x - 3a - y - z ][ 2x - 3a + y + z ]$
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