Factorise : 27x³ + y³ + z³ – 9xyz

Question

TextAlgebraic Identity for Sum of CubesNCERT Textbook

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

Factorise : 8x³ + y³ + 27z³ – 18xyz

Verify:

CASE_STUDIESAlgebraic Identity for Sum of CubesAlgebraic Identity for Difference of Cubes

Factorise each of the following:

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

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