Question

prove that (x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x) = 0

Answer 1

Given: The term (x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x) = 0

To find: Prove the above term.

Solution:

• Now we have given the term (x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x) = 0

• Lets consider LHS, we have:

• (x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x)

• Now we know the formula, which is:

              (a - b)(a + b) = a^2 - b^2

• So applying it in LHS, we get:

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

• Now adding it, we get:

              x^2 - y^2 + y^2 - z^2 + z^2 - x^2

              0   .............RHS.

Answer:

          So in solution part we proved that (x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x) = 0

Answer 2

agar ESE. hi ek question h (x-y) (x+y)+(y-z) (z-x) (z+x)

solve the following using identities