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Question
Factorise : 4x4 - x2 - 12x - 36
Solution
Factorise : 4x4 - x2 - 12x - 36
= 4x4 - ( x2 + 12x + 36 )
= ( 2x2)2 - ( x2 + 2x × 6x + 62 )
= ( 2x2)2 - ( x + 6 )2
= ( 2x2 + x + 6 )( 2x2 - x - 6 )
= ( 2x2 + x + 6 )( 2x2 - 4x + 3x - 6 )
= ( 2x2 + x + 6 )[ 2x( x - 2 ) + 3( x - 2 )]
= ( 2x2 + x + 6 )[ ( x - 2)( 2x + 3 )]
= ( 2x2 + x + 6 )( x - 2 )( 2x + 3 )
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