Question 51

$$(a + b + c - d)^2 - (a - b - c + d)^2 = ?$$

Solution

$$(a + b + c - d)^2 - (a - b - c + d)^2$$

[(a + b + c - d)+(a - b - c + d)][(a + b + c - d) - (a - b - c + d)]

($$\because a^2 - b^2 = (a + b)(a - b))$$

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

= 4a(b + c - d)

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