1. Simplifying Algebraic Expressions
RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match

2. Simplifying Algebraic Expressions
RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match
EXAMPLES :
- Like terms, can be combined
- Can NOT be combined, exponents are different..
- Can NOT be combined, two totally different terms
- Like terms, can be combined

3. Simplifying Algebraic Expressions
RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match
b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “
EXAMPLES :
Term DOES NOT change !!!

4. Simplifying Algebraic Expressions
RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match
b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “
EXAMPLES :
Term DOES NOT change !!!
ONLY combine the coefficients !!!

5. Simplifying Algebraic Expressions
RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match
b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “
c ) when a negative sign appears in front of a set of parentheses or brackets, change ALL the signs INSIDE the parentheses or brackets.
EXAMPLE :
It is just like you are multiplying ( - 1 ) by everything inside…

6. Simplifying Algebraic Expressions
RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match
b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like term “
c ) when a negative sign appears in front of a set of parentheses or brackets, change ALL the signs INSIDE the parentheses or brackets.
d ) when a positive sign appears in front of a set of parentheses or brackets, just drop the parentheses or brackets and keep the signs the terms already hold.
EXAMPLE :

7. Simplifying Algebraic Expressions
RULES : a ) when combining “like terms”, the variables AND their exponents must ALL match
b ) when combining like terms, the term DOES NOT change, only the coefficient does. Combine the coefficients of the “like terms “
c ) when a negative sign appears in front of a set of parentheses or brackets, change ALL the signs INSIDE the parentheses or brackets.
d ) when a positive sign appears in front of a set of parentheses or brackets, just drop the parentheses or brackets and keep the signs the terms already hold.
e ) when multiple parentheses and brackets are used, work from the INNER most bracket out

8. Simplifying Algebraic Expressions
EXAMPLE 1 :

9. Simplifying Algebraic Expressions
EXAMPLE 1 :
I like to draw little “walls” in between each term so I can see them better

10. Simplifying Algebraic Expressions
EXAMPLE 1 :
Next, make a list of the terms you see…and find the matches, combine coefficients.

11. Simplifying Algebraic Expressions
EXAMPLE 1 :
Next, make a list of the terms you see…and find the matches, combine coefficients.

12. Simplifying Algebraic Expressions
EXAMPLE 1 :
Next, make a list of the terms you see…and find the matches, combine coefficients.
I’ll also cross out the ones I just used… it helps you see “what’s left”…

13. Simplifying Algebraic Expressions
EXAMPLE 1 :
Next, make a list of the terms you see…and find the matches, combine coefficients.

14. Simplifying Algebraic Expressions
EXAMPLE 1 :
Looks like we got all of them.

15. Simplifying Algebraic Expressions
EXAMPLE 1 :
Your answer is right here...

16. Simplifying Algebraic Expressions
EXAMPLE 1 :
Your answer is right here...

17. Simplifying Algebraic Expressions
EXAMPLE 2 :

18. Simplifying Algebraic Expressions
EXAMPLE 2 :
OK, we have brackets and imbedded parens here. So again, we will work with the inner most parens first.

19. Simplifying Algebraic Expressions
EXAMPLE 2 :
Drop brackets and signs stay the same
Change signs in set 1

20. Simplifying Algebraic Expressions
EXAMPLE 2 :
Combine like terms inside both brackets

21. Simplifying Algebraic Expressions
EXAMPLE 2 :
Drop brackets and change signs

22. Simplifying Algebraic Expressions
EXAMPLE 2 :
Separate your terms

23. Simplifying Algebraic Expressions
EXAMPLE 2 :
ANSWER

24. Simplifying Algebraic Expressions
EXAMPLE 3 :

25. Simplifying Algebraic Expressions
EXAMPLE 3 :
OK, multiple imbedded brackets / parens. Start with the innermost set…

26. Simplifying Algebraic Expressions
EXAMPLE 3 :
Drop parens and change signs

27. Simplifying Algebraic Expressions
EXAMPLE 3 :
Combine like terms inside brackets

28. Simplifying Algebraic Expressions
EXAMPLE 3 :
Drop brackets and keep signs

29. Simplifying Algebraic Expressions
EXAMPLE 3 :
Combine like terms inside

30. Simplifying Algebraic Expressions
EXAMPLE 3 :
Drop brackets and change signs

31. Simplifying Algebraic Expressions
EXAMPLE 3 :
Combine like terms

32. Simplifying Algebraic Expressions
EXAMPLE 3 :
ANSWER