L29: Add/Subtract Like Terms

L29: Add and Subtract Like Terms

Topics

• Defn: variables, terms, coefficient, expression, like terms

• How do we add or subtract terms with variables?

Terms

• can be a single number

   $5\ \ \ \ -7\ \ \ \ \ \ \frac{1}{2}\ \ \ \ \ 0.5$  

• can be a variable  $a\ \ \ \ \ b\ \ \ \ c\ \ \ \ \ x\ \ \ \ \ y\ \ \ \ \ \ z$  

• can be the product of a number and a variable (can be more than one variable)

   $7x\ \ \ \ \ \ \frac{1}{2}z^4\ \ \ \ \ -0.5p\ \ \ \ \ \ -12xy^2d$  

• this is not a term 5x + 7

Multiple Choice

Is this a term

 $6x^5$  

• yes

• no

Multiple Choice

Is this a term

 $2x^5-9$  

• yes

• no

Multiple Choice

Given the term, what is the coefficient:

 $2x^5$  

• 5

• 2

• x

Multiple Choice

Given the term, what is the coefficient:

 $-5x^7$  

• -5

• 7

• x

Multiple Choice

Given the term, what is the coefficient:

 $x^{ }$  

• 1

• 0

• x

Like Terms

• variable and exponents are the same

• the coefficients can be different

Multiple Choice

True or False:
4 and 14 are like terms.

• True 
• False

Multiple Choice

True or False:
4x and x are like terms.

• True 
• False

Multiple Choice

are these like terms?

x²

x³

• yes

• no

Multiple Choice

are these like terms?

3x

6x

• yes

• no

Expressions

• are the addition and subtraction of terms

• there are no "=" signs

• Good:

   $5x-7\ \ \ \ \ \ \ \ \ \ \ \ \ 8x\ +\ 7y\ -\ 6z\ \ \ \ \ \ \ \ \ \ -x^2\ +2x$  

• Bad:  $5x\ -\ 7\ =\ 0$ 

Multiple Choice

Which one is an expression?

• 5x - 9 = 9

• 9x + 1 = 12

• 2x - 4

• 19 = 2d - 1

How many terms are in an expression?

• count the terms

• between addition/subtraction

Multiple Choice

How many terms are in the expression:

• 2

• 3

• 4

• 5

• 6

Multiple Choice

How many terms are in the expression:

• 2

• 3

• 4

• 5

• 6

Combine Like Terms (simplify)

• 
  

• 
  

Multiple Choice

Simplify the expression: 3x + 2x

• 5x
• x
• 6x
• 5

Multiple Choice

Simplify the expression: 7v + 2 + 12 + 2v

• 23
• 23v
• 9 + 14v
• 9v + 14

Multiple Choice

Simplify the expression: 2x + 1 + 7x 

• 10x
• 10
• 9x + 1
• 9 + 1x