Question
Simplify:
$12x - [3x^3+ 5x^2- {7x^2- (4 - 3x - x^3) + 6x^3} - 3x]$
$12x - [3x^3+ 5x^2- {7x^2- (4 - 3x - x^3) + 6x^3} - 3x]$
✓
Answer
Removing the innermost grouping symbol () first, then { } and then [ ], we have
$12 x-\left[3 x^3+5 x^2-\left\{7 x^2-\left(4-3 x-x^3\right)+6 x^3\right\}-3 x\right] $
$ =12 x-\left[3 x^3-5 x^2-\left\{7 x^2-4+3 x+x^3+6 x^3\right\}-3 x\right] $
$ =12 x-\left[3 x^3+5 x^2-\left\{7 x^2-4+3 x+7 x^3\right\}-3 x\right] $
$ =12 x-\left[3 x^3+5 x^2-7 x^2+4-3 x-7 x^3-3 x\right] $
$ =12 x-\left[3 x^3-7 x^3+5 x^2-7 x^2+4-3 x-3 x\right] $
$ =12 x-\left[-4 x^3+2 x^2+4-6 x\right] $
$ =12 x+4 x^3+2 x^2-4+6 x $
$ =12 x+6 x+4 x^3+2 x^2-4 $
$ =18 x+4 x^3+2 x^2-4 $
$ =4 x^3+2 x^2+18 x-4 $
$12 x-\left[3 x^3+5 x^2-\left\{7 x^2-\left(4-3 x-x^3\right)+6 x^3\right\}-3 x\right] $
$ =12 x-\left[3 x^3-5 x^2-\left\{7 x^2-4+3 x+x^3+6 x^3\right\}-3 x\right] $
$ =12 x-\left[3 x^3+5 x^2-\left\{7 x^2-4+3 x+7 x^3\right\}-3 x\right] $
$ =12 x-\left[3 x^3+5 x^2-7 x^2+4-3 x-7 x^3-3 x\right] $
$ =12 x-\left[3 x^3-7 x^3+5 x^2-7 x^2+4-3 x-3 x\right] $
$ =12 x-\left[-4 x^3+2 x^2+4-6 x\right] $
$ =12 x+4 x^3+2 x^2-4+6 x $
$ =12 x+6 x+4 x^3+2 x^2-4 $
$ =18 x+4 x^3+2 x^2-4 $
$ =4 x^3+2 x^2+18 x-4 $
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