Operations with Polynomials

Definition:
Like Terms : like terms have the same variable-exponent combination

Examples of like terms :

Examples of unlike terms :

Like terms are added and subtracted by adding or subtracting the coefficients .

Example: 3A+ 4A = 7A (think: 3 Apples + 4 Apples = 7 Apples)
Example: 12C − 9C = 3C (think: 12 Carrots – 9 Carrots = 3 Carrots)
Example: 7A+ 6O = 7A+ 6O (think: 7 Apples + 6 Oranges = 7 Apples + 6 Oranges, you can’t
add apples and oranges)
Example: 7A+ 8O+14 + 6A+ (−6) − 3O =13A+ 5O+ 8

You do not need like terms to perform multiplication or division . The coefficients are
multiplied ( or divided ). When multiplying, the exponents of variables are added . When
dividing , the exponents of variables are subtracted.

Example: 5(6x^2 − 7 y) = 30x^2 −35y (the 5 multiplies each term in the parentheses , this is known
as the distributive property )

Example:

Example:

Example:

In 1-20, perform the indicated operations .