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Question
Simplify:
(a + b)3 − a3 − b3
Simplify
Solution
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
(a + b)3 − a3 − b3
= (a + b)3 − (a3 + b3)
= (a + b)3 −{(a + b)(a2 + b2 − ab)}
= (a + b) {(a + b)2 − (a2 + b2 − ab)}
= (a + b) (a2 + b2 + 2ab − a2 − b2 + ab)
= (a + b) (3ab)
= 3a2b + 3ab2
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