Which of the following is a factor of

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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