Addition of Polynomials

• Two terms are considered like terms if they:1) are both constants, or

2) have the same variables with the same exponents on corresponding variables

• Recall the definition of like terms:

• The concept of like terms is important, since only like terms can be added together.

• Example 1:

Since the variables are the same with the same exponent, the terms are Like Terms.

5 6x xAdd:

You will recall that to add like terms, we use the distributive property.

5 6x x 5 6 x 11x

It is not necessary to write the middle step. Just do the addition in your head

• Example 2:

Since these are not like terms, they cannot be combined or added.

5 6xAdd:

• Example 3:

Since both terms have the same variables, with the same exponents on corresponding variables, they are Like Terms.

2 3 5 2 3 56 9x y z x y z Add:

2 3 5 2 3 56 9x y z x y z

2 3 56 9 x y z

2 3 53x y z

• Example 4:

Drop the parentheses and write with like terms together, and add.

2 22 4 3 5 7 8x x x x Add:

2 22 4 3 5 7 8x x x x

2 2 4 7 85 32 x xx x

27 3 5x x