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:
Answer: -11
