1. Combine Like Terms
I can simplify expressions with several variables by combining like terms.

2. Constant Vocabulary A number with nothing else attached to it.
Examples: 1, 2, 47, 925

3. Variable Vocabulary A letter that represents an unknown number.
Examples: a, b, x, y

4. Coefficient Vocabulary The number in front of the variable.
Examples: 3x is the coefficient
2x is the coefficient

5. Like Terms:
In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents).
Examples: 4x and -3x or 2y2 and –y2

6. Like terms because each term consists of a single variable, x, and a numeric coefficient:
2x, 45x, x, 0x, -26x, -x
Like terms because they are all constants:
15, -2, 27, 9043, 0.6
Like terms because they are all y² with a coefficient: 3y², y², -y², 26y²

7. What are unlike terms?
The following two terms both have a single variable, but the terms are not alike since different variables are used: 17x, 17z
Each y variable in the terms below has a different exponent, therefore these are unlike terms: 15y, 19y², 31y5
Although both terms below have an x variable, only one term has the y variable, thus these are not like terms either: 19x, 14xy

8. Combine Like Terms
I can simplify expressions with several variables by combining like terms.

9. Like Terms – same variable with same exponent
Key Skills
Like Terms – same variable with same exponent
Simplify
When combining like terms, only use the coefficients.
6x + 2x =
6x + 2x = 8x
Simplify
4x + 3y – 2x + 4y =
2x + 7y
Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.

10. 5 cats + 3 cats
8 cats

11. 5a + 3a 8a

12. 5 apples + 3 oranges
5 apples + 3 oranges

13. 5 cats + 3 dogs
5 cats + 3 dogs

14. You Try
3y x – y + 5x
x + x

15. The Distributive Property
Expressions with variables:
Simplify 5(3n + 4).
No symbol between the 5 and the parenthesis indicates a multiplication problem.
Distribute by multiplication:
15n and 20 are not alike and therefore cannot be combined. The answer 15n + 20 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.

16. The Distributive Property
Simplify 4(7n + 2) + 6.
No symbol between the 4 and the parenthesis indicates a multiplication problem.
The constant terms 8 and 6 can be combined to form the constant number 14. The answer 28n + 14 is simplified because we do not know what the value of n is at this time and cannot complete the multiplication part of this problem.

17. Distributive Property
Step 1) Use the Distributive Property 3 (2x – 5) - 2x
Step 2) Combine Like Terms 6x – 15 – 2x
*** 6x and 2x are like terms!!!!
Step 3) Simplified Expression 4x – 15

18. Distributive Property
Example:
6(a + 3) Use the Distributive Property
(6a) + (6 x 3) Multiply
6a Simplified
***CAN NOT add 6a + 18 together because they are not like terms.

19. Practice Problems Solve: 2x + 6(x + 1)
Explain how each of the below answers are wrong and why.
2x + 6x + 1 9x