### Addition
and Subtraction of Polynomials

Algebraic expressions with more than one term.

### See Terms

**Adding Polynomials
**

To add polynomials, you must clear the parenthesis, combine and add the like terms. In some cases you will need to remember the order of operations. Remember, when adding and subtracting like parts, the variable never changes.

Here are a couple of examples:

(5

x+ 7y) + (2x- 1y)= 5

x+ 7y+ 2x- 1y----- (Clear the parenthesis)=5

x+ 2x+ 7y- 1y----- (Combine the like terms)= 7

x +6y--- (Add like terms)

Another Example:

(

y^{2}- 3y+ 6) + (y- 3y2 +y^{3)}

y^{2}- 3y+ 6+y- 3y^{2 + y3 }---- (Clear the parenthesis)

y^{3 }+y^{2}- 3y^{2}- 3y+y+ 6----- (Combine the like terms)

y^{3 }- 2y^{2}- 2y^{ }+ 6---- (Add like terms)

**Subtracting
Polynomials**

To subtract polynomials, you must change the sign of terms being subtracted, clear the parenthesis, and combine the like terms. Here's an example:

(4

x(^{2}- 4) -x^{2}+ 4x- 4)(4

x(-^{2}- 4) +x^{2}- 4x+ 4) ---- (Change the signs)4

x-^{2}- 4 +x^{2}- 4x+ 4 ---- (Clear the parenthesis)4

x+ 4 -- ----- (Combine the like terms)^{2}-x^{2}- 4x- 4

3x^{2 }- 4x

Another Example:

(5x

^{2}+ 2x +1) - ( 3x^{2}– 4x –2 )5x

^{2}+ 2x +1 - 3x^{2}+ 4x +2 --(Change the signs and clear the parenthesis)5x

^{2}- 3x^{2}+ 2x+ 4x+1 + 2 --(Combine the like terms)2x

^{2}+ 6x +3

**Polynomial Definitions
of Terms:
**A monomial has one term: 5y or -8

*x*

^{2}or 3.

A binomial has two terms: -3

*x*

^{2}+ 2, or 9y - 2y

^{2}

A trinomial has 3 terms: -3

*x*

^{2}+ 2 +3x, or 9y - 2y

^{2}+ y

The degree of the term is the exponent of the variable: 3

*x*

^{2}has a degree of 2.

**When the variable does not have an exponent - always understand that there's a '1' e.g., 3**

^{x}**Related Links**: