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