Factor of (x + y)³ − (x³ + y³)
Which of the following is a factor of \[ (x+y)^3-(x^3+y^3)? \]
(a) \(x^2+y^2+2xy\)
(b) \(x^2+y^2-xy\)
(c) \(xy^2\)
(d) \(3xy\)
Solution
\[ (x+y)^3=x^3+y^3+3xy(x+y) \]
Therefore,
\[ (x+y)^3-(x^3+y^3)=3xy(x+y) \]
Hence,
\[ \boxed{(d)\ 3xy} \]