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SSC CHSL 2025 PYQ — Question 51

SSC CHSL - 29 Nov 2025 - Shift 3 • Quantitative Aptitude • Q51

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In a microchip design, expression for interference signal is [(x + y)² + (x - y)²]²  Find the simplified expression.

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Correct answer: C

Explanation

Given:

[(x + y)² + (x − y)²]²

According to the formulas:

[(x+y)2+(x−y)2]2=(x2+2xy+y2+x2−2xy+y2)2=(2x2+2y2)2=[2(x2+y2)]2=4(x2+y2)2=4(x4+2x2y2+y4)=4x4+8x2y2+4y4∴4x4+8x2y2+4y4 \left[(x+y)^2+(x-y)^2\right]^2 \\ =\left(x^2+2xy+y^2+x^2-2xy+y^2\right)^2 \\ =\left(2x^2+2y^2\right)^2 \\ =\left[2(x^2+y^2)\right]^2 \\ =4(x^2+y^2)^2 \\ =4(x^4+2x^2y^2+y^4) \\ =4x^4+8x^2y^2+4y^4 \\ \therefore\boxed{4x^4+8x^2y^2+4y^4} \\