Question

(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x) is equal to​

Answer 1

(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x)

x²+xy-xy-y²+y²+yz-yz-z²+z²+xz-xz-z²

* everything will get canceled *

so, 1 would be the answer

hope this would help

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Answer 2

SOLUTION

TO DETERMINE

The value of

(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x)

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

(x – y)(x + y) = x² - y²

EVALUATION

Here the given expression is

(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x)

We simplify it as below

(x – y)(x + y) + (y – z)(y + z) + (z – x) (z + x)

= x² - y² + y² - z² + z² - x²

= 0

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