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SSC CHSL 2023 PYQ — Question 67

SSC CHSL - 14 Aug 2023 - Shift 3 • Quantitative Aptitude • Q67

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Simplify the given expression. 

(x+3)3+(x−3)3(x2+27)\frac{(x+3)^3 + (x - 3)^3}{(x^2 + 27)} 

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 2x.

(x+3)3+(x−3)3(x2+27)\frac{(x+3)^3 + (x - 3)^3}{(x^2 + 27)}

=2x[(x2+6x+9)−(x2−9)+(x2−6x+9)](x3+27)=\frac{2x[(x^2 + 6x + 9) - (x^2 - 9) + (x^2 - 6x + 9)]}{(x^3+27)}

=2x(x2+6x+9−x2+9+x2−6x+9)(x3+27)=\frac{2x(x^2 + 6x + 9 - x^2 + 9 + x^2 - 6x + 9)}{(x^3+27)}

=2x(x2+27)(x3+27)=\frac{2x(x^2 + 27)}{(x^3+27)}

= 2x