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:

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

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

=5x + 2x + 7y - 1y ----- (Combine the like terms)

= 7x + 6y --- (Add like terms)

Another Example:

(y² - 3y + 6) + (y - 3y 2 + y³⁾

y² - 3y + 6+ y - 3y^{2 + y3} ---- (Clear the parenthesis)

y³ + y² - 3y² - 3y + y + 6----- (Combine the like terms)

y³ - 2y² - 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:

(4x² - 4) - (x² + 4x - 4)

(4x² - 4) + (-x² - 4x + 4) ---- (Change the signs)

4x² - 4 + -x² - 4x + 4 ---- (Clear the parenthesis)

4x² -x² - 4x- 4 + 4 -- ----- (Combine the like terms)

3x² - 4x

Another Example: 

(5x² + 2x +1) - ( 3x² – 4x –2 )

5x² + 2x +1 - 3x² + 4x +2 --(Change the signs and clear the parenthesis)

5x² - 3x² + 2x+ 4x+1 + 2 --(Combine the like terms)

2x²+ 6x +3

Polynomial Definitions of Terms:
A monomial has one term: 5y or -8x² or 3.
A binomial has two terms: -3x² + 2, or 9y - 2y²
A trinomial has 3 terms: -3x² + 2 +3x, or 9y - 2y² + y
The degree of the term is the exponent of the variable: 3x² has a degree of 2.
When the variable does not have an exponent - always understand that there's a '1' e.g., 3^x

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