Verify that x³ + y³ + z³ – 3xyz = 1/2 (x + y + z)[(x – y)² + (y – z)² + (z – x)²]

Question

TextAlgebraic Identity for Sum of CubesNCERT Textbook

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Factorise : 8x³ + y³ + 27z³ – 18xyz

Verify:

Factorise each of the following:

Factorise : 27x³ + y³ + z³ – 9xyz

If x + y + z = 0, show that x³ + y³ + z³ = 3xyz.

Without actually calculating the cubes, find the value of each of the following: