Which of the following is a factor of (x + y)³ – (x³+ y³)?
(a) x²+ y² + 2xy
(b) x²+ y² – xy
(c) xy²
(d) 3xy

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Solution

(x + y)³ – (x³+ y³)
$= x^{3} + y^{3} + 3 x y (x + y) - (x^{3} + y^{3}) = 3 x y (x + y)$
Thus, the factors of (x + y)³ – (x³+ y³) are 3xy and (x + y).
Hence, the correct answer is option (d).

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