Simplifying Expressions

Simplifying Expressions

Lesson 3.1

Poll

Given the problem 6x + 4 - 2x, your brother says the answer is 8x + 4. Is your brother correct? Be prepared to explain!

• yes

• no

Vocabulary

• Parts of an expression are called terms.

• Like terms are terms that have the same variables raised to the same exponent.

• Constants are numbers. They are also like terms.

Identifying Terms and Like Terms

• To identify terms and like terms, write the expression as a sum.

• Follow Keep, Change, Opposite

• 9x – 2 + 7 – x

• 9x + (-2) + 7 + (-x)

• Terms: 9x, -2, 7, -x

• Like terms: 9x, -x AND -2, 7

What about terms with exponents?

•  $y^2\ +5y\ -\ 3y^2\ +\ y$  

• Rewrite as addition.

•  $y^2\ +\ 5y\ +\ \left(-3y^2\right)\ +\ y$  

• Like terms:

•  $y^2,\ -3y^2\ AND\ 5y,\ y$ 

Multiple Choice

Identify the like terms.

 $y\ +\ 10\ -\ \frac{3}{2}y$  

•  $y,\ \frac{3}{2}y$  

•  $10,\ \frac{3}{2}y$  

•  $y,\ -\frac{3}{2}y$  

•  $10,\ -\frac{3}{2}y$  

Multiple Choice

Identify the like terms.

 $2r^2\ +\ 7r\ -\ r^2\ -\ 9$  

•  $2r^2,\ -r^2\$  

•  $2r^2,\ r^2$  

•  $2r^2,\ 7r,\ -r^2$  

•  $2r^2,\ 7r$  

Multiple Choice

Identify the like terms.

7 + 4p - 5 + p + 2y

• 4p, -5, 2y

• 4p, p, 2y

• 7, 5 AND 4p, p

• 7, -5 AND 4p, p

Simplifying an Algebraic Expression

• Simplify 3x + 5 – 6x - 2

• Rewrite as addition.

• 3x + 5 + (-6x) + (-2) 

• Combine like terms.

• 3x + (-6x) = -3x

• 5 + (-2) = 3

• -3x + 3

Simplifying an Algebraic Expression

• Simplify   $\frac{3}{4}y\ +\ 12\ -\ \frac{1}{2}y-\ 6$  

• Rewrite as addition.

•  $\frac{3}{4}y\ +\ 12\ +\ \left(-\frac{1}{2}y\right)\ +\ \left(-6\right)$  

• Combine like terms.

•  $\frac{3}{4}y\ +\ \left(-\frac{1}{2}y\right)=\frac{1}{4}y$  

• 12 + (-6) = 6

•  $\frac{1}{4}y\ +\ 6$  

Multiple Choice

Simplify the expression.

14 - 3z + 8 + z

• -2z + 22

• 2z + 22

• 4z + 22

• -4z + 22

Multiple Choice

Simplify the expression.

2.5x + 4.3x - 5

• 1.8x - 5

• 6.8x + 5

• 6.8x - 5

• 11.8x

Simplifying with the Distributive Property

• Simplify 4(-2x + 5) + 6x

• Distribute

• 4(-2x) + 4(5) + 6x 

• -8x + 20 + 6x

• Combine like terms

• -8x + 6x = -2x

• -2x + 20

Simplifying with the Distributive Property

• Simplify $-\frac{1}{2}\left(6n\ +\ 4\right)\ +\ 2n$  

  
  

• Distribute

• -½(6n) + -½(4) + 2n 

• -3n + (-2) + 2n

• Combine like terms    

• -1n + (-2)

• -n - 2

Multiple Choice

Simplify the expression.

3(q + 1) - 4

• 3q - 1

• 3q + 7

• 3q + 1

• 3q - 3

Multiple Choice

Simplify the expression.

-2(g + 4) + 7g

• 9g - 8

• 9g + 4

• 5g + 4

• 5g - 8

• Each person in a group buys a ticket, a medium drink, and a large popcorn. Write an expression in simplest form that represents the amount of money the group spends at the movies.

• 7.50x + 2.75x + 4x

• 14.25x

• The total cost for each person is $14.25.

Open Ended

What if each person buys a ticket, a large drink, and a small popcorn. How does the expression change?