would multiplying 3 negative integers always equal a positive integer?

no, it would never be positive.

multiplying two negatives always gives a positive. That third negative then yields a negative product.

no

To determine if multiplying three negative integers always results in a positive integer, we can use basic rules of arithmetic.

Remember that in multiplication, multiplying two negative numbers together results in a positive number. For example, (-2) multiplied by (-3) equals 6, which is positive.

So, if we have two negative numbers multiplied together, we know the result is positive.

Therefore, when multiplying three negative integers, the first two negative integers will result in a positive number. Then, this positive number will be multiplied by the third negative integer. The overall answer will depend on the third negative integer.

If the third negative integer is also negative, then multiplying the first two positive results (from the previous step) by the third negative integer will yield a positive integer.

If the third negative integer is positive, then multiplying the first two positive results by the third positive integer will yield a negative integer because a positive integer multiplied by a negative integer gives a negative result.

In summary, multiplying three negative integers will result in a positive integer if the third negative integer is also negative. If it is positive, the result will be negative.