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Which of the following is the value of [(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3] / [(x - y)^3 +…

Using the identity \(A^3 + B^3 + C^3 = 3ABC\) when \(A + B + C = 0\): Numerator \(= 3(x^2-y^2)(y^2-z^2)(z^2-x^2)\) and Denominator \(= 3(x-y)(y-z)(z-x)\). Dividing the two…

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Which of the following is the value of [(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3] / [(x - y)^3 + (y - z)^3 + (z - x)^3] ?

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Answer and explanation

Correct answer D

Using the identity A3+B3+C3=3ABCA^3 + B^3 + C^3 = 3ABC when A+B+C=0A + B + C = 0: Numerator =3(x2−y2)(y2−z2)(z2−x2)= 3(x^2-y^2)(y^2-z^2)(z^2-x^2) and Denominator =3(x−y)(y−z)(z−x)= 3(x-y)(y-z)(z-x). Dividing the two leaves (x+y)(y+z)(z+x)(x+y)(y+z)(z+x).

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