Answer: (i) a^3 - b^3 = 1 when a = 0 and b = -1.
(ii) a^2 + 2ab + b^3 = -3 when a = 0 and b = -1.
(iii) 3ab + 3ac + c^2 = 1 when a = 0, b = -1, and c = 1.
Step-by-step explanation:
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i) a^3 - b^3
When a = 0 and b = -1, we have:
a^3 - b^3 = 0^3 - (-1)^3 = 0 - (-1) = 1
Therefore, a^3 - b^3 = 1 when a = 0 and b = -1.
ii) a^2 + 2ab + b^3
When a = 0 and b = -1, we have:
a^2 + 2ab + b^3 = 0^2 + 2(0)(-1) + (-1)^3 = 0 - 2 + (-1) = -3
Therefore, a^2 + 2ab + b^3 = -3 when a = 0 and b = -1.
iii) 3ab + 3ac + c^2
When a = 0, b = -1, and c = 1, we have:
3ab + 3ac + c^2 = 3(0)(-1) + 3(0)(1) + 1^2 = 0 + 0 + 1 = 1
Therefore, 3ab + 3ac + c^2 = 1 when a = 0, b = -1, and c = 1.
I hope that helps! Let me know if you have any questions or if there's anything else I can do for you.