Simplify $a (a^{2} + a + 1) + 1$ and find its value for $a = 1$

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Solution

$a (a^{2} + a + 1) + 1$
$= a^{3} + a^{2} + a + 1$
$= a^{2} (a + 1) + 1 (a + 1)$
$= (a^{2} + 1) (a + 1)$ at $a = 1$
$= (1 + 1) (1 + 1)$
$= 2 \times 2 = 4$

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Question 4(b)
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