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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 + x2y – xy2 + y3
R.H.S. = x3 + y3
∴ R.H.S. = L.H.S.
Hence, verified.
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