(a + b + c − d)2 − (a − b − c + d)2 = ?

2a(b + c − d) 4a(b + c − d) 2a(b + c + d) 4a(b + c + d)

4a(b + c − d)

We know that, a2 - b2 = (a + b) (a – b) a = (a + b + c − d) b = (a − b − c + d) (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) = (2a) (2b + 2c - 2d) = 4a(b + c − d)