Simplifying Expressions

Simplifying Expressions

How can you simplify algebraic expressions?

Posing the Problem

Use what you know about variables and algebraic expressions to simplify this expression: $x+5+2x+2$  

 $x+5+2x+2$  

• Find like terms (terms that have the same variable).

• x and 2x both have the variable x. 

• 5 and 2 are both constants.

• Rewrite the expression with like terms together: x + 2x + 5 + 2

• Combine like terms: x + 2x = 3x

• Combine like terms: 5 + 2 = 7

• So, this expression is simplified to: 3x + 7

Multiple Choice

In this expression, which terms are LIKE TERMS?
 $a-4+5a$  

• a & -4

• -4 & 5a

• a & 5a

Multiple Select

Which terms are LIKE terms?

(Select all correct answers).
 $5y+8+2y-3$  

• 5y & 8

• 5y & 2y

• 8 & -3

• 2y & -3

Step Two: Rewrite the expression with LIKE TERMS together.

 $3x+2-x+7$  

• 3x & -x are like terms.

• 2 & 7 are like terms. 

• Rewrite with these terms together:

• 3x - x + 2 + 7

Multiple Choice

Rewrite this expression with LIKE TERMS together:

 $6b+7-2b+3$  

• 6b + 7 + 3 - 2b

• 7 - 2b + 6b + 3

• 6b - 2b + 7 + 3

Multiple Choice

Rewrite this expression with LIKE TERMS together:

 $5c+2m-m+8c$  

• 5c + 8c + 2m - m

• 5c - m + 8c + 2m

• 8c - m + 2m + 5c

• 2m + 5c - m + 8c

STEP THREE: 

Combine Coefficients in Like Terms

 $7d-2d+8-5$  

• Combine 7d & -2d: 7 - 2 = 5d

• Combine 8 & -5: 8 - 5 = 3

• So, expression is: 5d + 3

Multiple Choice

Combine the Coefficients of these LIKE TERMS:

 $8m-3m$  

• 11m

• 5m

• 83m

• 5

Multiple Choice

Combine the Coefficients of these LIKE TERMS:

 $6x+7x$  

• x

• 13

• 13x

• 67x

Now, let's try it all together:

 $7d+8-2d+6$  

• 1. Find LIKE TERMS: 7d & -2d are LIKE. 8 & 6 are LIKE.

• 2. Rewrite with LIKE TERMS together: 7d - 2d + 8 + 6

• 3. Combine the coefficients of the LIKE TERMS: 7d - 2d = 5d, and 8 + 6 = 14.

• Simplified Expression = 5d + 14

Multiple Choice

Simplify this expression:

 $4y-8+4y$  

• 8

• 44y - 8

• 8y - 8

• 8y + 8

Multiple Choice

Simplify this expression:

 $6x+5-3x$  

• 9x + 5

• 9x - 5

• 3x - 5

• 3x + 5

Poll

How are you feeling about Simplifying Expressions?

• Great!

• So-So

• Confused