Type your response in the box. simplify these algebraic expressions:
12x + 3 − 4x + 7

8 − 7x − 13 + 2x

−3x − 18 + 5x − 2

Fun problem.

We have a positive product, so no zero factors.

We have a positive product, so an even number of negative factors.

We have a product of 1, so all the integers must be either +1 or -1.

If we have 2n factors of -1 we have 22-2n factors of 1 so a sum of

For that to be zero we need

That's not an integer; we've shown there's no even number of -1s that will make the sum zero, and since there must be an even number of -1s, the sum cannot equal zero.