Question:
Which of the following is a factor of \[ (x+y)^3-(x^3+y^3)? \]
(a) \(x^2+2xy+y^2\)
(b) \(x^2-xy+y^2\)
(c) \(xy^2\)
(d) \(3xy\)
Solution:
\[ (x+y)^3-(x^3+y^3) \]
\[ =x^3+3x^2y+3xy^2+y^3-x^3-y^3 \]
\[ =3x^2y+3xy^2 \]
\[ =3xy(x+y) \]
Hence, one factor is
\[ \boxed{3xy} \]