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SSC CHSL 2023 PYQ — Question 59

SSC CHSL - 04 Aug 2023 - Shift 4 • Quantitative Aptitude • Q59

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Simplify the following expression. (a2+b2−c2)2−(a2−b2+c2)2b2−c2\frac{(a^2+b^2-c^2)^2- (a^2-b^2+c^2)^2}{b^2-c^2}

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. 4a2.

Given that 

(a2+b2−c2)2−(a2−b2+c2)2b2−c2\frac{(a^2+b^2-c^2)^2- (a^2-b^2+c^2)^2}{b^2-c^2}

Formula used

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Calculation

⇒ (a4+b4+c4+2a2b2−2b2c2−2c2a2)−(a4+b4+c4−2a2b2−2b2c2+2c2a2)b2−c2\frac{(a^4+b^4+c^4+2a^2b^2 -2b^2c^2 -2c^2a^2)- (a^4+b^4+c^4-2a^2b^2 -2b^2c^2 +2c^2a^2)}{b^2-c^2}

⇒ 4a2b2−4c2a2b2−c2\frac{4a^2b^2 -4c^2a^2}{b^2-c^2}

⇒ 4a2(b2−c2)b2−c2\frac{4a^2(b^2 -c^2)}{b^2-c^2}

⇒ 4a2