Simplify, giving the answers in factors:
$(a + 1) (a - 18) + (a - 2) (a + 15)$

2 (a - 6) (a - 4)

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2 (a - 6) (a + 4)

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2 (a - 4) (a + 6)

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2 (a + 6) (a + 4)

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Solution

The correct option is B $2 (a - 6) (a + 4)$
$\Rightarrow (a + 1) (a - 18) + (a - 2) (a + 15)$
$\Rightarrow (a^{2} + a - 18 a - 18) + (a^{2} - 2 a + 15 a - 30)$
$\Rightarrow a^{2} - 17 a - 18 + a^{2} + 13 a - 30$
$\Rightarrow 2 a^{2} - 4 a - 48$
$\Rightarrow 2 (a^{2} - 2 a - 24)$
$\Rightarrow 2 (a^{2} - 6 a + 4 a - 24)$
$\Rightarrow 2 (a (a - 6) + 4 (a - 6))$
$\Rightarrow 2 (a - 6) (a + 4)$

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