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:
$ 5 a-\left[a^2-\left\{2 a\left(1-a+4 a^2\right)-3 a\left(a^2-5 a-3\right)\right\}\right]-8 a $
$ =5 a-\left[a^2-\left\{2 a-2 a^2+8 a^3-3 a^3+15 a^2+9 a\right\}\right]-8 a $
$ =5 a-\left[a^2-\left\{2 a+9 a-2 a^2+15 a^2+8 a^3-3 a^3\right\}\right]-8 a $
$ =5 a-\left[a^2-\left\{11 a+13 a^2+5 a^3\right\}\right]-8 a $
$ =5 a-\left[a^2-11 a-13 a^2-5 a^3\right]-8 a $
$ =5 a-a^2+11 a+13 a^2+5 a^3-8 a $
$ =5 a+11 a-8 a-a^2+13 a^2+5 a^3 $
$ =8 a+12 a^2+5 a^3 $
$ =5 a 3+12 a^2+8 a $
$ 5 a-\left[a^2-\left\{2 a\left(1-a+4 a^2\right)-3 a\left(a^2-5 a-3\right)\right\}\right]-8 a $
$ =5 a-\left[a^2-\left\{2 a-2 a^2+8 a^3-3 a^3+15 a^2+9 a\right\}\right]-8 a $
$ =5 a-\left[a^2-\left\{2 a+9 a-2 a^2+15 a^2+8 a^3-3 a^3\right\}\right]-8 a $
$ =5 a-\left[a^2-\left\{11 a+13 a^2+5 a^3\right\}\right]-8 a $
$ =5 a-\left[a^2-11 a-13 a^2-5 a^3\right]-8 a $
$ =5 a-a^2+11 a+13 a^2+5 a^3-8 a $
$ =5 a+11 a-8 a-a^2+13 a^2+5 a^3 $
$ =8 a+12 a^2+5 a^3 $
$ =5 a 3+12 a^2+8 a $
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