Question
Simplify:
$5a - [a^2 - {2a(1 - a + 4a^2) - 3a(a^2 - 5a - 3)}] - 8a$
$5a - [a^2 - {2a(1 - a + 4a^2) - 3a(a^2 - 5a - 3)}] - 8a$
✓
Answer
Removing the innermost grouping symbol ( ) first, then { } and then [ ], we have:
$5a - [a^2 - {2a (1 - a + 4a^2) - 3a (a^2 - 5a - 3)}] - 8a$
$= 5a - [a^2 - {2a - 2a^2 + 8a^3 - 3a^3 + 15a^2 + 9a}] - 8a$
$= 5a - [a^2 - {2a + 9a - 2a^2 + 15a^2 + 8a^3 - 3a^3}] - 8a$
$= 5a - [a^2 - {11a + 13a^2 + 5a^3}] - 8a$
$= 5a - [a^2 - 11a - 13a^2 - 5a^3] - 8a$
$= 5a - a^2 + 11a + 13a^2 + 5a^3 - 8a$
$= 5a + 11a - 8a - a^2 + 13a^2 + 5a^3$
$= 8a + 12a^2 + 5a^3$
$= 5a3 + 12a^2 + 8a$
$5a - [a^2 - {2a (1 - a + 4a^2) - 3a (a^2 - 5a - 3)}] - 8a$
$= 5a - [a^2 - {2a - 2a^2 + 8a^3 - 3a^3 + 15a^2 + 9a}] - 8a$
$= 5a - [a^2 - {2a + 9a - 2a^2 + 15a^2 + 8a^3 - 3a^3}] - 8a$
$= 5a - [a^2 - {11a + 13a^2 + 5a^3}] - 8a$
$= 5a - [a^2 - 11a - 13a^2 - 5a^3] - 8a$
$= 5a - a^2 + 11a + 13a^2 + 5a^3 - 8a$
$= 5a + 11a - 8a - a^2 + 13a^2 + 5a^3$
$= 8a + 12a^2 + 5a^3$
$= 5a3 + 12a^2 + 8a$
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