Simplify : $(a^{3} - 2 a^{2} + 4 a - 5) - (- a^{3} - 8 a + 2 a^{2} + 5)$ .

2 a^{3} + 7 a^{2} + 6 a - 10

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2 a^{3} + 7 a^{2} + 12 a - 10

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2 a^{3} - 4 a^{2} + 12 a - 10

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2 a^{3} - 4 a^{2} + 6 a - 10

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Solution

The correct option is C $2 a^{3} - 4 a^{2} + 12 a - 10$
We need to simplify $(a^{3} - 2 a^{2} + 4 a - 5) - (- a^{3} - 8 a + 2 a^{2} + 5)$
$= a^{3} - 2 a^{2} + 4 a - 5 + a^{3} + 8 a - 2 a^{2} - 5$
$= (a^{3} + a^{3}) + (- 2 a^{2} - 2 a^{2}) + (4 a + 8 a) - 10$
$= 2 a^{3} - 4 a^{2} + 12 a - 10$

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