2018 · Q10
If x + y + z = 0, then what is (y + z - x)³ + (z + x - y)³ + (x + y - z)³ equal to?
Elementary MathematicsAlgebra
- A(x + y + z)³
- B3(x + y)(y + z)(z + x)
- C24xyz
- D-24xyz
Explanation
Since x + y + z = 0, each bracket equals −2x, −2y, −2z respectively. The sum of their cubes is −8(x³ + y³ + z³). The identity x³ + y³ + z³ = 3xyz (valid when x + y + z = 0) gives −8 × 3xyz = −24xyz, option (D).