2022 · Q35
If x = b + c, y = c + a, z = a + b, then what is (x + y + z)³ - 24xyz equal to?
Elementary MathematicsAlgebra
- Aa³ + b³ + c³
- B2 (a³ + b³ + c³)
- C8 (a³ + b³ + c³)
- DNone of the above
Explanation
x+y+z = 2(a+b+c). Using (a+b+c)³ = a³+b³+c³+3(a+b)(b+c)(c+a): (x+y+z)³−24xyz = 8(a+b+c)³ − 24(a+b)(b+c)(c+a) = 8(a³+b³+c³). The keyed option is C.