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1. $a^{3} - 9 + {(a + 1)}^{3}$

Answer: Option A

Explanation:

a^{3} - 9 + {(a + 1)}^{3} = a^{3} - 9 + a^{3} + 3 a^{2} + 3 a + 1 = 2 a^{3} + 3 a^{2} + 3 a - 8 = 2 a^{3} - 2 a^{2} + 5 a^{2} - 5 a + 8 a - 8 = 2 a^{2} (a - 1) + 5 a (a - 1) + 8 (a - 1) = (2 a^{2} + 5 a + 8) (a - 1)

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