(-x %2B z)^3 %2B (x - y)^3 %2B (y - z)^3

1.	(-x %2B z)^3 %2B (x - y)^3 %2B (y - z)^3
Answer» a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ac)when a + b + c = 0a³ + b³ + c³ - 3abc = 0=> a³ + b³ + c³ = 3abc Let a = x - yb = y - zc = z - xa + b + c = x - y + y - z + z - x => the above equation turns out to be 3(x - y)(y - z)(z - x)Expand it to find the answer (-3x²y + 3xy² + 3x²z - 3y²z - 3xz² + 3yz²)

Answer»

a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ac)when a + b + c = 0a³ + b³ + c³ - 3abc = 0=> a³ + b³ + c³ = 3abc

Let a = x - yb = y - zc = z - xa + b + c = x - y + y - z + z - x

=> the above equation turns out to be 3(x - y)(y - z)(z - x)Expand it to find the answer (-3x²y + 3xy² + 3x²z - 3y²z - 3xz² + 3yz²)

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