1. Simplifying and Evaluating Expressions

2. Simplifying Expressions
When simplifying, look for like terms
Like terms are terms that contain the same variables raised to the same power.
Coefficients do not need to be the same in order to combine terms. Variables MUST be the same though!

3. Examples! 
Look at the following terms and list all like terms

4. Solution! -8x2y, 3x2y, -1/3x2y -4/5xy2,-2xy2, 4xy2 -7x2yz 1/3xy 2x2y2
All these terms have x2y
All these terms have xy2
This is the only x2yz term
This is the only xy term
All these terms have x2y2
This is the only xy2z term

5. A word of caution….
Be very careful when combining terms, x2yz and xy2z might look similar but we can’t combine them! That’s like saying apples and oranges are the same!

6. Examples! 3x + 6x 8x + 4y - 5x - 7y 10x - x - 9x + x
13 + 5t + 6y - t - y - 2
a - 4a
8x - 5x y - y - 1 9x
3x-3y
-8x
11+4t+5y
-3a
3x+2+y

7. Simplify the Following Expressions
2xy2+y2x+3x+4
3xy2+3x+4
5xyz-4x2+3xyz-9+10x2
8xyz+6x2-9
4x2+3xy+2x2+y
6x2+3xy+y

8. Evaluating Expressions
We already know that variables can be numbers, therefore we are allowed to substitute values into expressions and then perform said operations….this is known as evaluating

9. Evaluate! Evaluate the expression 4x+2x when x=3. 4x+2x
4(3)+2(3) Substitute the value of x
12+6 Perform multiplication
18 Simplify to get answer

10. Now you try!  3y+2y when y=3 4x2-3 when x=2 2x2+2x-3 when x=3
3(3)+2(3)=9+6=15
4(22)-3=4(4)-3=16-3= 13
2(3)2+2(3)-3=2(9)+2(3)-3
=18+6-3=21