Some special cases that are relevant in practice are:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
(x + a)(x + b) = x2 + (a+b)x + ab
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(w - 1)2
It depends on the product of sum of what.
The answer depends on the level of mathematics. With complex numbers, it is the squared magnitude of the binomial.
No, it is not.
use long division.