Question

What is the identity of x²+y²+z²

Answer 1

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(x+ y+z)²= (x+y+z) (x+y+z)

= x(x+y+z)+y(x+y+z)+z(x+y+z)

=x²+xy+xz+yx+y²+yz+zx+zy+z²

=x²+y²+z²+2xy+2yz+2zx

_________ OR ________

Let x+y = A

So, (x+y+z)² becomes (A+z)²

But by identity , (a+b)² = a² + b² + 2ab

So,

(A+z)² = A² + z² + 2Az

Now substituting A = x + y in (A+z)² = A² + z² + 2Az

(x+y+z)² = (x+y)² + z² + 2*(x+y)*z

(x+y+z)² = (x+y)² + z² + 2xz + 2yz

But, (x+y)² = x² + y² + 2xy

So,

(x+y+z)² = x² + y² + 2xy + z² + 2xz + 2yz

Therefore ,

(x+y+z)²

= x² + y² + z² + 2xy + 2xz + 2yz

Answer 2

Rocky singh thank you