1. 5.2 Like and Unlike Terms

2. Zero Pairs
When you work with integers, if you combine -1 and +1, it would be zero.
What do you think happens when you combine algebra tiles with opposite signs?
A 1 tile and a –1 tile form a zero pair.
We can use zero pairs to simplify polynomials.

3. Write the integer modeled by each set of tiles.
= ________
= ________ +2 -3

4. Terms that can be represented by algebra tiles with the same size and shape are called like terms.
Like terms have the same variables, and/or the same exponent.
Like terms: x2 and –2x2; 4s and –s;
6 and –2
Unlike terms: 3s and s2; 2x and –5;
3d2 and 7

5. Simplify this tile model.
Write the polynomial that the remaining tiles represent.

6. To simplify: First, we group like tiles.
Identify and remove the zero pairs.
The tiles that remain are:
They represent: x2 + x - 2
When there is only 1 of a type of tile, we omit the coefficient “1”.

7. We can also simplify a polynomial by adding the coefficients of the like terms. This is called combining like terms.
-x2 + 3x2
-1x2 + 3x2 = 2x2
A polynomial in simplified form is a polynomial in which all the like terms have been combined.

8. Simplify each polynomial.
5d d – 1 = 5d + 3d + 2 – 1 = 8d + 1 2a2 – 3a + 5a2 + 7a = 2a2 + 5a2 – 3a + 7a = 7a2 + 4a
Remember:
Group the like terms.
Add the coefficients of the like terms , or combine them.

9. A polynomial may contain more than one variable.
Example: 4xy – y2 – 3x2 + 2xy – x – 3y2
We follow the same process. Group the like terms, (the variables must be the same letters to be like terms).
= 4xy + 2xy – y2 –3y2 – 3x2 – x
= 6xy – 4y2 – 3x2 - x

10. Polynomials can represent situations.
Write a polynomial that represents the perimeter and area of each rectangle.
 3x  x x 1

11. Assignment:
Pg. 222: 4, 5, 8, 9, 11 ace, 18a, 12ace, 13ace, 14ace, 22