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Any negative integer can be factored to -1 times its positive value. Because negative one times itself is positive one, when multiplied by each other they cancel out.

So if you're multiplying a negative integer A by a negative integer B. Replace A and B with -1*|A| and -1*|B| (You can do this because you know A and B are negative), and use the distributive property to rearrange them. Now you can see the -1*-1 term and equate it to 1, leaving only the |A| and |B| behind. Because two positive numbers multiplied together are always positive, the result will always be positive.

Represented algebraically, as long as A and B are negative integers, the following is true:

AB = -1|A|*-1|B| = -1*-1|AB| = |AB|.

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