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Evaluate abs(-4 b - 8) + abs(-b^2 - 1) + 2 b^3 where b = -2:

abs(-4 b - 8) + abs(-b^2 - 1) + 2 b^3 = abs(-4 (-2) - 8) + abs(-1 - (-2)^2) + (-2)^3×2

(-2)^2 = 4:

abs(-4 (-2) - 8) + abs(-4 - 1) + 2×(-2)^3

-4 (-2) = 8:

abs(8 - 8) + abs(-4 - 1) + 2×(-2)^3

8 - 8 = 0:

abs(0) + abs(-1 - 4) + 2×(-2)^3

-1 - 4 = -5:

abs(0) + abs(-5) + 2×(-2)^3

(-2)^3 = (-1)^3×2^3 = -2^3:

abs(0) + abs(-5) + 2×-2^3

2^3 = 2×2^2:

abs(0) + abs(-5) + 2 (-2×2^2)

2^2 = 4:

abs(0) + abs(-5) + 2 (-2×4)

2×4 = 8:

abs(0) + abs(-5) + 2 (-8)

Since 0 is at the origin, then abs(0) = 0:

abs(-5) - 8×2

Since -5<=0, then abs(-5) = 5:

5 - 8×2

2 (-8) = -16:

-16 + 5

5 - 16 **= -11**

Guest Sep 18, 2017