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

• Terms are separated by a  +  or  -  sign

• The expression below has 4 TERMS:

•         4x - 2y + 5 - xyz

Fill in the Blanks

2) The expression below contains

terms.

$-3x^2+y-2-x^3$  

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

Fill in the Blanks

6) What is the LARGEST CONSTANT found in the expression?

$2b^5+1\ -6a+4.2$  

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

Complete the following problems in your homework packet as notes:

Multiple Choice

Combine like terms:

2x - 4 + 2x - 10

• 4x + 14

• 4x + 6

• 6

• 4x -14

Multiple Choice

Combine like terms:

2x + 3y - 5x - 9y - 8xy -2x

• 8xy + (-5x) + (-6y)

• 9x + 12y + 8xy

• -19xy

• 9x + (-6y) + 8xy

Multiple Choice

Combine like terms:

2x + 2x + x + x

• 4x + 2x

• 6x

• 4x

Multiple Choice

Combine like terms:

8xy + 8x - 6y + 2xy - 10x

• 10xy - 2x - 8y

• 10xy + 18x - 6y

• 2xy

• 10xy + (-2x) + (-6y)

Multiple Choice

Combine like terms:

5x + 5y + x - x + 8x

• 20xy

• 13x + 5y

• 15x + 5y

• 13x + 7y

Multiple Choice

Combine like terms:

x + 4 + x - 2x + 4

• 4x + 8

• 2x + 8

• 12x

• 8

Multiple Choice

Combine like terms:

2x + 3x + 9 + x

• 5x + 9

• 14x

• 6x + 9

• 15x

Multiple Choice

Combine like terms:

-4x - 20 - 20 + 8x

• 12x + 40

• 12x

• 4x + (-40)

• -36x

Multiple Choice

Combine like terms:

4x + 17 - 5x - 5x + x

• 5x + 17

• 12

• 32x

• 12x

Complete & submit your homework.

Show your work on the paper.

Take a picture and upload to Canvas.