Is 8x^2 + x^2 - 7x - x + 2x + 5y - 3y equal to 9x^2 - 8x + 2y or 9x^2 - 6x + 2y?
When adding polynomials, group like terms (which have identical powers of variables).
(8x^2 + x^2) + (- 7x - x + 2x) + (5y - 3y)
notice how the x terms were grouped, preserving all the signs.
The first group (8x²+x²) would give 9x² with no ambiguity.
The same is true of the last group, where (5y - 3y) = 2y
To work out the middle group, the number line can be a big help:
******-10x***-8x***-7x***-6x*********0***
Note that a negative number is to the left of zero, and that adding moves to the right ->, and subtracting (or adding a negative number) moves to the left <-.
Now focus on the middle group:
(- 7x - x + 2x)
Start with -7x on the number line.
-x is negative, so move left one unit to -8x.
+2x is positive, so move two units to the right to get -6x.
So the answer for the middle group is -6x.
If you follow these steps for adding/subtracting expressions involving negative numbers, you will have no difficulties in getting the correct answers.