### Question 18

SSC-CGL 2020 Mar 3 Shift 2

Simplify (a + b + c + d)² - (a - b - c - d)²

### Solution in Brief

Let $\displaystyle x = (a + b + c + d)^2 $

Let $\displaystyle y = (a - b - c - d)^2 $

We know from algebra that

$\displaystyle x^2 - y^2 = (x - y)(x + y)$

So the given expression becomes

$\displaystyle (2b + 2c + 2d)(2a)$

$\displaystyle =4a(b + c + d)\:\underline{Ans}$

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