3. Terms that have exactly the same variable factors
Like Terms
Terms that have exactly the same variable factors
45x^2 & x^2
2s & 9m
-8z & 5
-25 &
-u & u
3po & r^2d^2
Like
Not Like

4. 2x, 45x, x, 0x, -26x, -x Combining like terms.
To combine like terms you pretty much do exactly what the name tells you to. You combine or add up all of the like terms.
Each of the following are like terms because they are all x with a coefficient.
2x, 45x, x, 0x, -26x, -x

5. Each of the following are like terms because they are all constants.
Combining like terms.
Each of the following are like terms because they are all constants.
15, -2, 27, 9043, 0.6
Each of the following are like terms because they are all y^2 with a coefficient.
3y^2, y^2, -y^2, 26y^2

6. Examples of unlike terms.
For comparison, below are a few examples of unlike terms.
The following two terms are both variables but because they are different letter variables, they are unlike terms.
17x, 17z

7. Examples of unlike terms.
The following terms are all the same letter, but each variable has a different power or exponent.
15y, 19y^2, 31y^5
The following two terms both have the variable y but the second term has another variable in it, therefore they are unlike terms.
19x, 14xy

8. The expression which we will be simplifying is below.
x + 3x + 7
1.) The first step is to find which terms can be added. You can only add like terms
2.) The x and 3x are like terms, so they are added and become 4x. (HINT: when a variable such as x has no coefficient, its coefficient is 1 so x is the same as 1x.)
3.) The 7 does not have a like term, so it can be left alone.
4x + 7

9. 42 + x - 12
This time there is no term which can be added with x
There are two constants: 42 and -12.
When added they become 30.
x + 30

10. 3 – 5(a-4) 3 – 5a + 20 23 – 5a OR -5a +23 Use distributive property
There is no term which can be added with a
There are two constants: 3 and 20.
23 – 5a OR
-5a +23
When added they become 23.
Terms with variables are written first and in alphabetical order, and the constants are written last

11. Which algebraic expression is equivalent to the expression below
Which algebraic expression is equivalent to the expression below? 8(2x + 6) - 14

12. Which algebraic expression is equivalent to the expression below?

13. Simplify the following expression
Combine Like Terms
7.9x + (-4.83x)
= 3.07x

14. Which algebraic expression is equivalent to the expression below
Which algebraic expression is equivalent to the expression below? 4(3x + 9) + 7x - 14

15. Factoring – Opposite of Distributive
To factor the expression, factor out the greatest common factor of 1/4x and 15/4.
The greatest common factor is 1/4 .

16. Factor the expression completely
To factor the expression, factor out the greatest common factor of -20x and -40.
The greatest common factor is -20.

17. Factor the expression completely
The greatest common factor is

18. Simplify the following expression
7/21x + 15/21x = 22/21x
-5/7 +4/7 = -1/7

19. Simplify the following expression
7.6x +4.02x = 11.62x
= 4.31

20. Expand the following expression (Distribute)
Should be written as x

21. Which algebraic expression is equivalent to the expression below
Which algebraic expression is equivalent to the expression below? (3x + 6) + 3(11 - x)