x^2+y^2+z^2÷xy-yz-zx
if x=1 y=-2 z=3
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We will work with the RHS part here,
(x + y+ z)( x² +y² +z² - xy - yz - zx)
Expanding the entire bracket,
= x³ + xy² + xz² - x²y - xyz -zx² + yx + y³ + yz² - xy² - y²z - xyz + zx² + zy² + z³ - xyz - yz² - z²x
=x³ + y³ +z³ - 3xyz
This is equal to LHS
Hence proved
(x + y+ z)( x² +y² +z² - xy - yz - zx)
Expanding the entire bracket,
= x³ + xy² + xz² - x²y - xyz -zx² + yx + y³ + yz² - xy² - y²z - xyz + zx² + zy² + z³ - xyz - yz² - z²x
=x³ + y³ +z³ - 3xyz
This is equal to LHS
Hence proved
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