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) +