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Question
Evaluate: (a + 1)(a2 - a + 1) and (a - 1)(a2 + a + 1)
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Solution
(a + 1)(a2 - a + 1) and (a - 1)(a2 + a + 1)
= a (a2 - a + 1) + 1 (a2 - a + 1)
= a3 - a2 + a + a2 - a + 1
= a3 + 1
(a - 1)(a2 + a + 1)
= a(a2 + a + 1) - 1(a2 + a + 1)
= a3 + a2 + a - a2 - a - 1
= a3 - 1
Now, (a + 1)(a2 - a + 1) + (a - 1)(a2 + a + 1)
= a3 + 1 + a3 - 1
= 2a3
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