Question:
Which of the following is a factor of $(x+y)^{3}-\left(x^{3}+y^{3}\right)$ ?
(a) $x^{2}+y^{2}+2 x y$
(b) $x^{2}+y^{2}-x y$
(c) $x y^{2}$
(d) $3 x y$
Solution:
$(x+y)^{3}-\left(x^{3}+y^{3}\right)$
$=x^{3}+y^{3}+3 x y(x+y)-\left(x^{3}+y^{3}\right)$
$=3 x y(x+y)$
Thus, the factors of $(x+y)^{3}-\left(x^{3}+y^{3}\right)$ are $3 x y$ and $(x+y)$.
Hence, the correct answer is option (d).
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