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Question
Factorise : (x2 + 4y2 - 9z2)2 - 16x2y2
Solution
(x2 + 4y2 - 9z2)2 - 16x2y2
= (x2 + 4y2 - 9z2)2 - ( 4xy )2
= ( x2 + 4y2 - 9z2 - 4xy )( x2 + 4y2 - 9z2 + 4xy ) [ ∵ a2 - b2 = ( a + b )( a - b )]
= ( x2 + 4y2 - 4xy - 9z2 )( x2 + 4y2 + 4xy - 9z2 )
= [( x - 2y )2 - (3z)2 ][ ( x + 2y )2 - (3z)2 ]
= [( x - 2y ) - 3z ][( x - 2y ) + 3z ][( x + 2y ) - 3z ][( x + 2y ) + 3z ]
= [ x - 2y - 3z ][ x - 2y + 3z ][ x + 2y - 3z ][ x + 2y + 3z ]
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