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Question
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
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Solution
x3 − y3 = (x − y)(x2 + xy + y2)
L.H.S. = x3 − y3
Consider the right-hand side (RHS) and expand it as follows:
R.H.S. = (x − y)(x2 + xy + y2)
R.H.S. = x(x2 + xy + y2) − y(x2 + xy + y2)
R.H.S. = x3 + x2y + xy2 − yx2 − xy2 − y3
R.H.S. = (x3 − y3) + (x2y + xy2 + x2y − xy2)
R.H.S. = x3 − y3
∴ R.H.S. = L.H.S.
Hence, verified.
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