Parts of an Expression and Combining Like Terms

COMBINING

LIKE-TERMS

* What are some key vocab words?

* How do you identify like-terms?

* How do you "combine" like-terms?

VOCAB REVIEW

• Expression

• Term

• Variable

• Coefficient

• Constant

• Like-Term

• Combine Like-Terms
  

EXPRESSION

• A "math problem" that may contain:

• Numbers

• Letters (variables)

• Addition or Subtraction

• Multiplication or Division
  

• Exponents

• It DOES NOT contain an   =   sign
  (usually gets "simplified" , not solved)

Multiple Select

1) Which of these can be found in a math expression?

• addition

• multiplication

• exponents

• variables

TERM

• The individual "parts" of an expression

• Each term starts with a   +   or   -    sign

• The expression below has 4 TERMS:

•                4x - 2y + 5 - xyz

VARIABLE

• The LETTER part of a term

• 'x' is the most commonly used

• Represents an unknown value

• The value of 'x' will vary/change from problem to problem

• VARIABLE TERM - refers to the entire term that contains the variable

Multiple Choice

3) In the expression below, what is the 2ND VARIABLE TERM?

$$\ \ \ 2x\ -\ 3\ -5x^2\ -\ 1$$  

• 2x

• -3

• $$-5x^2$$  

• -1

COEFFICIENT

• A number connected to THE FRONT OF A VARIABLE TERM

• Always include the sign...is it positive or negative?

• Every variable has a coefficient, even if you can't see it

• Think of the prefix: "co"

• EXAMPLE:  -2x + 5 - y + 3

    The  coefficients are: -2 and -1 (invisible)

Multiple Select

4) Which of these choices is a COEFFICIENT found in the expression:

$$-2\ -5a\ +\ 1\ -6b^3$$  

• -2

• 5

• a

• -6

• 3

Multiple Select

5) What is the FIRST COEFFICIENT that appears in the expression:

$$y\ +2-4x^5y\ -\ 3c^2$$  

• 1

• y

• -4

• 5

• -3

CONSTANTS

• A number NOT connected to a variable

• Always include the sign...is it positive or negative?

• Constants can be whole numbers, decimals, or fractions

• All constants are like-terms

• EXAMPLE: -2x + 5 - y + 3                

• The constants are: +5 and +3

LIKE-TERMS

• Have the EXACT SAME VARIABLE part

• The exponents must also match

• All constants are like-terms

• Positive or negative has no effect

• Only like-terms can be "combined"

Multiple Select

7) Which of the pairs listed are LIKE-TERMS?

• $$2x\ \&\ 2y$$  

• $$-5x\ \&\ -2$$  

• $$+3b\ \&\ +3bc$$  

• $$a^2\ \&\ a^3$$  

• NONE

Multiple Select

8) Which of the pairs listed are LIKE-TERMS?

• $$-3\ \&\ -3.25$$  

• $$\frac{3}{4}x\ \ \&\ \ \frac{1}{2}x$$  

• $$-5b^2\ \ \&\ \ +b^2$$  

• $$s^2t\ \ \ \&\ \ \ st^2$$  

COMBINE

LIKE-TERMS

• Add or subtract matching pieces

• Use the signs IN FRONT

• Do NOT combine everything!

• Do NOT change exponents!

• WARNING: x + y  does not become  xy

• It doesn't combine at all!

Multiple Select

9) Which of the pairs listed can be COMBINED?

• $$2x\ \&\ 2y$$  

• $$-5x\ \&\ -2$$  

• $$+3b\ \&\ +3bc$$  

• $$a^2\ \&\ a^3$$  

• NONE

Multiple Select

10) When COMBINING LIKE-TERMS, you can:

• add

• subtract

• multiply

• divide