The factor of x³- x²y-xy²+y³, are
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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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