how do you add and subtract polynomials?

1. 4y + 5 - 8 = 4y - 3
2. -x^2 + 3x - 5x - 2x^2 = -3x^2 - 2x
3. 4k^2 +8k +2 -2k - 3 = 4k^2 +6k -1

4. something is missing here. it's the open parenthesis ' ( '.

1)
(4y + 5) + (-7 - 1)
= 4y + 5 - 7 - 1
= 4y - 2 - 1
= 4y - 3

2)
(-x^2 + 3x) - (5x + 2x^2)
= -x^2 + 3x - 5x - 2x^2
= -x^2 - 2x^2 - 2x
= -3x^2 - 2x

3)
(4k^2 + 8k + 2) - (2k + 3)
= 4k^2 + 8k + 2 - 2k - 3
= 4k^2 + 8k - 2k + 2 - 3
= 4k^2 + 6k - 1

4)
(2m^2 + 6m) + (m^2 - 5m + 7)
= 2m^2 + 6m + m^2 - 5m + 7
= 2m^2 + m^2 + 6m - 5m + 7
= 3m^2 + m + 7

1. (4y + 5 + (-7 - 1)
= 4y + 5 - 7 - 1 : you clear parentheses, and put like terms together
= 4y - 3 : then add and subtract like terms

2. (-x^2 + 3x) - (5x + 2x^2)
= -x^2 + 3x - 5x - 2x^2 : to clear a parenthesis with a negative out front, change all the signs inside
= -x^2 - 2x^2 + 3x - 5x : put like terms together
= -3x^2 - 2x : then add and subtract like terms

3. (4k^2 + 8k + 2) - (2k + 3)
= 4k^2 + 8k + 2 - 2k - 3 : negative outside
= 4k^2 + 8k - 2k + 2 - 3 : group like terms
= 4k^2 + 6k - 1 : add and subtract

4. (2m^2 + 6m) + (m^2 - 5m + 7)
= 2m^2 + m^2 + 6m - 5m + 7 : clear parentheses and group like terms in one step
= 3m^2 + m + 7

here use this website it really helped me...
http://www.purplemath.com/modules/polyadd.htm

You do all the like terms together.

Let me give a simple example: I have 4 bananas and 3 strawberries. You have 6 bananas and 1 strawberry. When you add the two bunches together, you only add like terms. In this case, together we have 4+6 = 10 bananas, and 3+1 = 4 strawberries.

The terms in the equations are the same -- x is a different "fruit" than x^2, than x^3, etc. So, you only add like terms. All the terms in front of x go together, all the terms in front of x^2 go together, all the terms not in front of a variable go together, etc.