Verified answer

Given :

[tex] = (x + y)(x - y) + (y + z) \\ (y - 2) + (z + x)(z - x) \\ + 7[/tex]

Solution Explanation :

[tex] = (x + y)(x - y) + (y + z) \\ (y - 2) + (z + x)(z - x) \\ + 7 \\ \\ = {x}^{2} - {y}^{2} + y(y - 2) \\ + z(y - 2) + {z}^{2} - {x}^{2} + 7 \\ \\ = {x}^{2} - {y}^{2} + {y}^{2} - 2y + zy \\ - 2z + {z}^{2} - {x}^{2} + 7 \\ \\ = {\cancel{ {x}^{2} }} - {\cancel{ {x}^{2} }} - {\cancel{ {y}^{2} }} + {\cancel{ {y}^{2} }} - 2y \\ - 2z + {z}^{2} + 7 \\ \\ = - 2y - 2z + {z}^{2} + 7[/tex]

= (x + y)(x - y) + (y + z) (y - 2) + (z + x)(z - x) +7

= x ^ 2 - y ^ 2 + y(y - 2) z(y - 2) + z ^ 2 - x ^ 2 + 7

- 2z + z ^ 2 - x ^ 2 + 7 = x ^ 2 - y ^ 2 + y ^ 2 - 2y + zy

= x ^ 2 - x ^ 2 - y ^ 2 + y ^ 2 - 2y - 2z + z ^ 2 + 7

= - 2y - 2z + z ^ 2 + 7