Question 53

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

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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