Difference. A sum is the result of adding two numbers, and a difference is the result of subtracting two numbers.
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The product is the "sum" of a multiplication math problem.
If the opposite is meant to be the additive opposite and not the multiplicative opposite, then their sum is zero. The reason is that is what defines an additive opposite!
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"sum" means addition.... +
If by "opposite" you mean "additive inverse", the sum is zero. For example, 5 + (-5) = 0.