Classwork/Notes: Adding and Subtracting Polynomials
Adding and Subtracting Monomials
Just as you can perform operations on numbers, you can perform operations on polynomials. To add or subtract polynomials, combine like terms.
Add or subtract.
Examples:
15m3 + 6m2 + 2m3 =
15m3 + 6m2 + 2m3 =
15m3 + 2m3 + 6 m2 =
17m3+ 6m2
3x2 + 5 - 7x2 + 12
3x2 + 5 - 7x2 + 12 =
3x2- 7x2 + 5 + 12 =
-4x2 + 17
0.9y5 - 0.4y5 + 0.5x5 + y5
0.9y5 - 0.4y5 + 0.5x5 + y5 =
0.9y5 - 0.4y5 + y5 + 0.5x5 =
1.5y5 + 0.5x5
2 x2y - x2y - x2y
2x2y - x2y - x2y =
2x2y - x2y - x2y
0
Forms of Solving Addition or Subtraction with Polynomials
Polynomials can be added in either vertical or horizontal form.
In vertical form, align the like terms and add:

In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms:

Adding Polynomials
Add.
Examples:
(2x2 - x) + (x2 + 3x - 1)
(2x 2 - x) + (x2 + 3x - 1) =
(2x2 - x) + (x2 + 3x - 1) =
(2x2 + x2) + (-x + 3x) + (-1) =
3x2 + 2x – 1
(-2ab + b) + (2ab + a)
(-2ab + b) + (2ab + a) =
(-2ab + 2ab) + b + a =
0 + b + a = b + a
(4b5 + 8b) + (3b5 + 6b - 7b5 + b)
(4b5 + 8b) + (3b5 + 6b - 7b5 + b) =

15b
(20.2y2 + 6y + 5) + (1.7y2 - 8)
(20.2y2 + 6y + 5) + (1.7y2 - 8) =

21.9 y2 + 6y – 3
Subtracting Polynomials
To subtract polynomials, remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial, you must write the opposite of each term in the polynomial: -(2x3 - 3x + 7) = -2x3 + 3x - 7
Subtract.
Examples:
(2x2 + 6) - (4x2) =
(2x2 + 6) + (-4x2) =
(2x2 + 6) + (-4x2) =
(2x2 - 4x2) +