Which of the following is a factor of $(x + y)^{3} - (x^{3} + y^{3})$ ?

(a) $x^{2} + y^{2} + 2 x y$

(b) $x^{2} + y^{2} - x y$

(c) $x y^{2}$

(d) $3 x y$

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Solution

$(x + y)^{3} = x^{3} + y^{3} + 3 x y (x + y) (x + y)^{3} - (x^{3} + y^{3}) = 3 x y (x + y)$

Hence $3 x y$ is a factor

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