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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Solution

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

$= 5 a - [a^{2} - {2 a (1 - a + 4 a^{2}) - 3 a^{3} + 15 a^{2} + 9 a} - 8 a$

$= 5 a - [a^{2} - {2 a - 2 a^{2} + 8 a^{3} - 3 a^{3} + 15 a^{2} + 9 a} - 8 a$

$= 5 a - [a^{2} - {11 a + 5 a^{3} + 13 a^{2}} - 8 a$

$= 5 a - [a^{2} - 5 a^{3} - 13 a^{2} - 11 a] - 8 a$

$= 5 a + 5 a^{3} + 11 a + 12 a^{2} - 8 a$

$= 12 a^{2} + 5 a^{3} + 8 a$

$= 5 a^{3} + 12 a^{2} + 8 a$

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