Question

 (x - y)(x +y) + (y - z)(y +z) + (z - x)(z + x) = ​

Answer 1

Answer:

xy(x−y)+yz(y−z)+zx(z−x)

=(x×x×y)−(x×y×y)+(y×y×z)−(y×z×z)+(z×z×x)−(z×x×x)

→x

2

y−xy

2

+y

2

z−yz

2

+z

2

x−zx

2

Answer 2

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

By using identities:

$\bold{x^2-y^2}$

Therefore,

$\sf{x^2-y^2+y^2-z^2+z^2-x^2}$

Therefore,

$\sf{x^2}$ and $\sf{-x^2}$ will cut out..

Now,

$\sf{-y^2}$ and $\sf{y^2}$ will cut out..

Similarly,

$\sf{-z^2}$ and $\sf{z^2}$ will cut out..

Hence, we get 0