Question

factorize 8x cube - (2x-y) whole cube?

Answer 1

8x^3-(2x-y)^3
=(2x)^3-(2x-y)^3
=[2x-(2x-y)][(2x)^2-2x*(2x-y)+(2x-y)^2]
=[2x-2x-y][4x^2-4x^2+2xy+4x^2-4xy+y^2]
=(-y)[4x^2-2xy+y^2]

Answer 2

8x3 - (2x - y)3
= (2x)3 - (2x - y)3 
= { 2x - (2x - y) } { (2x)2+ 2x (2x- y ) + (2x - y )2 }                      [ as  a3 - b3 = (a-b)(a2 + ab +b2 )  ]
= { 2x- 2x + y } { 4x2 + 4x2 -2xy + 4x2 - 4xy + y2 }
 = { y } { 12x2 - 6xy + y2}


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