Question

Verify x3-y3 =(x-y)(x2 +xy +y2)

Answer 1

RHS = (x-y) (x2 + xy + y2)
= x3 + x2y + xy2 - x2y - xy2 - y3
= x3 - y3
this is equal to LHS
Hence Proved or verified

Answer 2

.  R.H.S => (x+y) ( x2 - xy + y2)
=> x3 - x2y + xy2 + x2y - xy2 + y3              
{On multiplying x3 + y3 with (x+y) ( x2 - xy + y2)}
=> [x3 + y3] + ( -x2y + x2y) + ( xy2 - xy2)
=>  x3 + y3
Since R.H.S = L.H.S,
That is x3 + y3 = x3 + y3
Hence, verified that
x3 + y3 = (x+y) ( x2 - xy + y2)

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