Simplifying Expressions

Simplifying Expressions

EQ: How do i identify the structure of an expression to rewrite it as the simplified equivalent?.

Like Terms

• Terms that have identical variable and exponents.

• In the expression 3x + 7 – 4x -2

   3x and -4x are like terms

    7 and -2 are like terms

• If a variable has no number in front of it, the coefficient is 1.

• We can combine like terms using addition or subtraction.

Open Ended

On the previous slide, we saw that 3x and -4x are like terms. We also saw that 7 and -2 are also like terms. Please explain why you think they are like terms?

Vocabulary:

Distributive Property

• Multiplying the number or variable on the outside of the parenthesis to each term inside the parenthesis

• 
  
   $3\left(4b\ -\ 8\right)\$  
  

•  $\ 3\left(4b\right)\ -\ 3\left(8\right)\$  

•  $12b\ -24$  

Multiple Choice

 $-12\left(m\ +4n\ -5p\right)$ 

Using Distributive Property, simplify this expression 

•  $-12m\ +48n\ +60p$  

•  $12m\ +48n\ -60p$  

•  $-12m\ -8n\ -17p$  

•  $-12m\ -48n\ +60p$  

Putting It All Together: How To Rewrite an Equivalent Simplified Expression

• Step 1: Use Distributive Property to get rid of all parenthesis (if possible)

• Step 2: Identify the like terms (same variable & same exponent)

• Step 3: Rewrite the problem putting like terms together (DON'T FORGET THE SIGN IN FRONT OF THE NUMBER (+/_))

• Step 4: Combine Like Terms

• Step 5: Check your work!!!!!

Multiple Select

 $2x\ +8-12-9x$  

What is the first step to simplifying this expression?

• Subtract 8 and -12

• Rewrite the problem 

• Identify the like terms

• Add 2x and -9x

Ex. 1

 $2x\ +8-12-9x$  

Step 1:  No parenthesis
Step 2:  Like Terms: 2x & -9x, 8 & -12
Step 3:  Rewrite:   $2x\ -9x\ +8-12$  
Step 4: Combine :  $-7x\ -4$  
Step 5:  Check CORRECT!!

Multiple Choice

Simplify 5(2 - 7n)

• 52 - 57n

• 10 - 7n

• 10 - 35n

• 10 + 35n

Multiple Choice

Simplify:
20x + 27y + 38y + 29x

• 49y + 64x
• 49y + 65x
• 49x + 65y
• 49x - 65y

Multiple Choice

-7(w-4)+3w - 27

• 10w + 21

• -4w + 1

• 3w + 5

• 2w - 5

Open Ended

Using the following sentence structure below, tell me how did you feel about the lesson and the presentation.

After today's lesson, I feel like .....