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Question
Factorise: (x - y)3 - 8x3
Sum
Solution
( x - y )3 - 8x3
= ( x - y )3 - ( 2x )3
= ( x - y - 2x )[ (x - y)2 + 2x(x - y) + (2x)2 ]
[ Using identity (a3 - b3) = (a - b)(a2 + ab + b2) ]
= (- x - y ) [ x2 + y2 - 2xy + 2x2 - 2xy + 4x2 ]
=- ( x + y ) [ 7x2 - 4xy + y2 ]
shaalaa.com
Method of Factorisation : the Sum Or Difference of Two Cubes
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