Question

To verify the algebraic identity (x+y+z)2 = x2+y2+z2+2xy +2yz +2zx

Answer 1

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

Answer:

Step-by-step explanation:

(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