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SSC CHSL 2025 PYQ — Question 73

SSC CHSL - 12 Nov 2025 - Shift 3 • Quantitative Aptitude • Q73

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Simplify: (x+y)3+(y+z)3+(z+x)3−3(x+y)(y+z)(z+x)x3+y3+z3−3xyz\frac{(x+y)^3+(y+z)^3+(z+x)^3-3(x+y)(y+z)(z+x)}{x^3+y^3+z^3-3xyz}

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Correct answer: B

Explanation

(x+y)3+(y+z)3+(z+x)3−3(x+y)(y+z)(z+x)x3+y3+z3−3xyz\frac{(x+y)^3+(y+z)^3+(z+x)^3-3(x+y)(y+z)(z+x)}{x^3+y^3+z^3-3xyz}
According to the formula:
a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)
(x + y)³ + (y + z)³ + (z + x)³ − 3(x + y)(y + z)(z + x)
= 2(x³ + y³ + z³ − 3xyz)
= 2(x³ + y³ + z³ − 3xyz) / (x³ + y³ + z³ − 3xyz)
= 2