Question

(x-y)(x+y)+(y-z)(y+z)+(z-x)(z+x)​

Answer 1

Question:

$(x - y)(x + y) + (y - z)(y + z) + (z - x)(z + x)$

Answer:

We know,

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

So, by implementing this identity, we get

$(x - y)(x + y) = {x}^{2} - {y}^{2} \\ (y -z )(y + z) = {y}^{2} - {z}^{2} \\ (z- x)(z +x ) = {z}^{2} - {x}^{2}$

Then we put these values in the equation.

$= {x}^{2} - {y}^{2} + {y}^{2} - {z}^{2} + {z}^{2} - {x}^{2} \\ = {x}^{2} - {x}^{2} + {y}^{2} - {y}^{2} + {z}^{2} - {z}^{2} \\ = 0$