Question

14. Prove that:
(a) (x + y)(x - y) + (y + 2)(y – z) + (z + x)(z - x) = 0​

Answer 1

refer to the attachment

hope it helps

Answer 2

Explanation:

$Hi! \\ \\ \bf To \ prove, \\ \boxed{\bf (x + y)(x - y) + (y + z)(y -z) + (z + x)(z - x) = 0} \\\\ \\LHS\\=>x(x-y)+y(x-y)+y(y-z)+z(y-z)+z(z-x)+x(z-x) \\\\ =>x^2-xy+xy-y^2+y^2-yz+yz-z^2+z^2-zx+zx-x^2\\ \\=> 0 = RHS \\\\ \bf [or] \\\\ \text{you can also use the identity and solve} \\\\ \boxed{[(a+b)(a-b)=a^2-b^2]} \\\\\\ \bf hope \ it \ helps..!$