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Question
Factorise : 3x7y - 81x4y4
Sum
Solution
3x7y - 81x4y4
= 3xy( x6 - 27x3y3 )
= 3xy[ (x2)3 - ( 3xy )3 ]
= 3xy( x2 - 3xy )[ (x2)2 + x2 x 3xy + (3xy)2 ] [ ∵ a3 - b3 = ( a -b )( a2 + ab + b2 )]
= 3xy( x2 - 3xy )[ x4 + 3x3y + 9x2y2 ]
= 3xy [ x( x + 3y) x2( x2 + 3xy + 9y2 ) ]
= 3x4y( x - 3y )( x2 + 3xy + 9y2 )
shaalaa.com
Method of Factorisation : the Sum Or Difference of Two Cubes
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