Subtract $a^{3} - 4 a^{2} + 5 a - 6$ from the sum of $3 a^{3} + a^{2} + 1$ and $a^{2} - 2$

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Solution

Let,

$p = a^{3} - 4 a^{2} + 5 a - 6$

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

$r = a^{2} - 2$

According to the question,

$\Rightarrow 3 a^{3} + a^{2} + 1 + a^{2} - 2 - (a^{3} - 4 a^{2} + 5 a - 6)$

$\Rightarrow 3 a^{3} + 2 a^{2} - 1 - a^{3} + 4 a^{2} - 5 a + 6$

$\Rightarrow 2 a^{3} + 6 a^{2} - 5 a + 5$

Hence, this is the answer.

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Solve

$5 a - [a^{2} - {2 a (1 - a + 4 a^{2}) - 3 a (a^{2} - 5 a - 3)}] - 8 a$

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