formula of x^3+y^3+z^3
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(ii)Without finding the cubes, factorise (x – y)3 + (y – z)3 + (z – x)3. Solution : We know that x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx). If x + y + z = 0, then x3 + y3 + z3 – 3xyz = 0 or x3 + y3 + z3 = 3xyz. (i) We have to find the value of 483 – 303 – 183 = 483 + (–30)3 + (–18)3.
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