Question

Verify that x³ + y² + z³ − 3xyz = (x + y + z)[(x − y)² + (y − x)²+(z - x)²].​

Answer 1

Answer:

We have, L.H.S.=x  

3

+y  

3

+z  

3

−3xyz

=(x+y+z)(x  

2

+y  

2

+z  

2

−xy−yz−zx)           [by poynomial identity]

=  

2

1

​

(x+y+z)(2x  

2

+2y  

2

+2z  

2

−2xy−2yz−2zx)

=  

2

1

​

[(x+y+z)(x−y)  

2

+(y−z)  

2

+(z−x)  

2

]

Hence proved.

Step-by-step explanation:

Answer 2

Answer:

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