Factorise the following:
(a + b)3 - a - b
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(a + b)3 - a - b = (a + b)3 - (a + b).
Taking out common in all terms,
(a + b)[(a + b)2 - 1].
Using identity,
a2 - b2 = (a - b)(a + b).
(a + b)[(a + b)2 - 1] = (a + b)(a + b - 1)(a + b + 1).
Hence, (a + b)3 - a - b = (a + b)(a + b - 1)(a + b + 1).
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2x4 - 32
a2(b + c) - (b + c)3
x2 - 2xy + y2 - a2 - 2ab - b2.
(a2 - b2)(c2 - d2) - 4abcd