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-2-\left(-5\left(-\left(4-\left(-8+4\right)\right)\right)\right)
Subtract 3 from -5 to get -8.
-2-\left(-5\left(-\left(4-\left(-4\right)\right)\right)\right)
Add -8 and 4 to get -4.
-2-\left(-5\left(-\left(4+4\right)\right)\right)
The opposite of -4 is 4.
-2-\left(-5\left(-8\right)\right)
Add 4 and 4 to get 8.
-2-40
Multiply -5 and -8 to get 40.
-42
Subtract 40 from -2 to get -42.