Subtract the sum of $(8 a - 6 a^{2} + 9)$ and $(- 10 a - 8 + 8 a^{2})$ from $- 3$ is _________.

2 a^{2} - 2 a - 2

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2 a^{2} - 2 a + 4

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- 2 a^{2} + 2 a - 4

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- 2 a^{2} + 2 a - 2

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Solution

The correct option is C $- 2 a^{2} + 2 a - 4$
$- 3 - [(8 a - 6 a^{2} + 9) + (- 10 a - 8 + 8 a^{2})]$

$= - 3 - [8 a - 6 a^{2} + 9 + - 10 a - 8 + 8 a^{2}]$

$= - 3 - [(8 a - 10 a) + (- 6 a^{2} + 8 a^{2}) + (9 - 8)]$

$= - 3 - [- 2 a + 2 a^{2} + 1]$

$= - 3 + 2 a - 2 a^{2} - 1$

$= + 2 a - 2 a^{2} - 4$

$= - 2 a^{2} + 2 a - 4$

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