Question

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4. Prove that (x - y) (x + y) + (y - z) (y + z) + (z - x) (2 + x) = 0
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Answer 1

Answer:

Step-by-step explanation:

L.H.S. =

$(x - y) (x + y) + (y - z) (y + z) + (z - x) (z + x)~~~(~\because~ a^2-b^2 = (a-b)(a+b)~)\\= (x^2-y^2) + (y^2-z^2)+(z^2-x^2)\\= (x^2-x^2)+(y^2-y^2)+(z^2-z^2)\\= 0$

= R.H.S.