Given: x+y+z=10 xy+yz+zx=18 Formula used: The expression for the sum of cubes of three numbers can be expressed as: x3+y3+z3−3xyz=(x+y+z)[(x+y+z)2−3(xy+yz+zx)] Calculation: Substituting the given values: x3+y3+z3−3xyz=(10)[(10)2−3(18)] ⇒x3+y3+z3−3xyz=10[100−54] ⇒x3+y3+z3−3xyz=10×46 ⇒x3+y3+z3−3xyz=460
