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Question
Factorise : 4x2 - 12ax - y2 - z2 - 2yz + 9a2
Sum
Solution
4x2 - 12ax - y2 - z2 - 2yz + 9a2
= 4x2 + 9a2 - 12ax - y2 - z2 - 2yz
= ( 2x )2 + ( 3a )2 - 12ax - ( y2 + z2 + 2yz )
= ( 2x - 3a )2 - ( y + z )2
= [( 2x - 3a ) - ( y + z )][( 2x - 3a ) + ( y + z )]
[ ∵ a2 - b2 = ( a + b )( a - b )]
= [ 2x - 3a - y - z ][ 2x - 3a + y + z ]
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Method of Factorisation : Difference of Two Squares
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