What is the Formula of x³+y³+ z³–3xyz

Answer:

(x + y + z) (x² + y² + z² – xy – yz – zx)

Verification 

To Prove: x³+y³+ z³–3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx)

Let the values of x, y and z be 2, 4 and 3 respectively.

Considering the L.H.S.,

L.H.S. = x³+y³+ z³–3xyz

Or 2³+4³+ 3³–3(2)(4)(3)

Or 8 + 64 + 27 – 72

Or 27

Now, considering the R.H.S.,

R.H.S. = (x + y + z) (x² + y² + z² – xy – yz – zx)

Or (2 + 4 + 3) (2² + 4² + 3² – (2)(4) – (4)(3) – (3)(2))

Or (9) (4 + 16 + 9 – 8 – 12 – 6)

Or (9) (29 – 26)

Or (9) (3)

Or 27

Hence verified.