Simplification and Combining Terms: Master Algebraic Expressions and Like Terms

Section	Expression
First Leg	$x$
Second Leg	$3 x + 7$
Third Leg	$4 x - 6$

Section

Expression

First Leg

x

Second Leg

3 x + 7

Third Leg

4 x - 6

	Saturday's Visitors
	Children	Adults
Before Noon	$7$	$12$
After Noon	$12$	$20$

Saturday's Visitors

Children

Adults

Before Noon

7

12

After Noon

12

20

	Sunday's Visitors
	Children	Adults
Before Noon	$8$	$15$
After Noon	$3$	$4$

Sunday's Visitors

Children

Adults

Before Noon

8

15

After Noon

3

4

	Saturday's Visitors
	Children $($)$	Adults $($)$	Total $($)$
Before Noon	$7 x$	$12 x^{2}$	$7 x + 12 x^{2}$
After Noon	$12 y$	$20 y^{2}$	$12 y + 20 y^{2}$

Saturday's Visitors

Children

($)

Adults

($)

Total

($)

Before Noon

7 x

12 x^{2}

7 x + 12 x^{2}

After Noon

12 y

20 y^{2}

12 y + 20 y^{2}

	Sunday's Visitors
	Children $($)$	Adults $($)$	Total $($)$
Before Noon	$8 x$	$15 x^{2}$	$8 x + 15 x^{2}$
After Noon	$3 y$	$4 y^{2}$	$3 y + 4 y^{2}$

Sunday's Visitors

Children

($)

Adults

($)

Total

($)

Before Noon

8 x

15 x^{2}

8 x + 15 x^{2}

After Noon

3 y

4 y^{2}

3 y + 4 y^{2}

	Vases $($)$	Plush Toys $($)$	Paintings $($)$	Total $($)$
First Group	$3 a$	$4 b$	$5 c$	$3 a + 4 b + 5 c$
Second Group	$- 2 a$	$6 b$	$1 c$	$- 2 a + 6 b + 1 c$
Third Group	$1 a$	$0$	$- 1 c$	$1 a - 1 c$

Vases

($)

Plush Toys

($)

Paintings

($)

Total

($)

First Group

3 a

4 b

5 c

3 a + 4 b + 5 c

Second Group

- 2 a

6 b

1 c

- 2 a + 6 b + 1 c

Third Group

1 a

0

- 1 c

1 a - 1 c

Davontay and his friends want to get ice cream.

Their favorite place, the Ice Cream Home, has the following prices.

Ice Cream Home Menu
Item	Price $($)$
Medium Ice Cream Sundae	$x$
Large Ice Cream Sundae	$2 x$
add $1$ topping	add $$ 1.00$
add $2$ toppings	add $$ 1.50$
add $3$ toppings	add $$ 2.00$

The friends placed the following order.

Two medium ice cream sundaes with $3$ toppings
One large ice cream sundae with $1$ topping
Four medium ice cream sundaes with $2$ toppings
Three medium ice cream sundaes without toppings

Write and simplify an expression for the total amount of money that Davontay's group will pay.

We are given the menu for ice cream sundaes at the Ice Cream Home. Prices vary depending on the size and number of toppings on the sundae.

Ice Cream Home Menu
Item	Price ($)
Medium Ice Cream Sundae	x
Large Ice Cream Sundae	2x
add 1 topping	add $ 1.00
add 2 toppings	add $ 1.50
add 3 toppings	add $ 2.00

We want to find the an expression for how much money the friends paid for their ice cream. Let's review their order.

Two medium ice cream sundaes with 3 toppings
One large ice cream sundae with 1 topping
Four medium ice cream sundaes with 2 toppings
Three medium ice cream sundaes without toppings

The friends can be divided into four groups based on their orders. Let's write the price of a single order from each group and then multiply these by the number of people who made that order. We can organize the information in a table.

	Price of a Single Order ($)	Total Group Price ($)
Group 1	x+2.00	2(x+2)
Group 2	2x+1.00	1(2x+1)
Group 3	x+1.50	4(x+1.5)
Group 4	x	3x

Now that we have an expression for each different order, we can find the total by adding all the expressions. 2(x+2)+ 2x+1 + 4(x+1.5) + 3x Let's simplify this expression. Remember to use the Distributive Property to simplify the terms between parentheses first.

Now that we have used the Distributive Property, we need to group like terms and add them. Let's do it!

The group paid a total of $11x+11 for the entire order. We did it!

Ali wants to create on a short film for a festival. He decides to rent the equipment he needs. The cost to rent the equipment is shown below.

Item	Daily Rental Cost $($)$	Down Payment $($)$
Camera Kit	$300$	$150$
Audio Kit	$250$	$100$
Lighting Kit	$100$	$30$

Write an expression for the total amount of money that Ali needs to rent everything he wants for

d

days.

We are told that Ali needs to rent equipment for d days to shoot a short film. We are asked to write an expression that can be used to represent the total cost. Let's take a look at the cost of each piece of equipment.

Item	Daily Rental Cost ($)	Down Payment ($)
Camera Kit	300	150
Audio Kit	250	100
Lighting Kit	100	30

Let's start by finding the total cost of renting the camera kit for d days. The rental fee is $ 300 per day. If Ali wants to rent the camera kit for d days, he will pay the product of d and $ 300. 300 d However, that is not the whole fee. Ali will also need to pay an additional down payment of 150. Let's add this to our expression. 300 d + 150 This is the total cost to rent the camera kit for d days. Let's write the costs of the other pieces of equipment in a similar way. We can organize this information in the table.

Item	Daily Rental Cost ($)	Down Payment ($)	Cost for d Days ($)
Camera Kit	300	150	300 d + 150
Audio Kit	250	100	250 d+ 100
Lighting Kit	100	30	100 d+ 30

Finally, let's add the costs of each piece of equipment to write an expression for the total cost of the rental. Remember to group the like terms together to combine them and simplify the expression.

Ali will have to pay $650d+280 to be able to shoot his dream project. Good job!

Consider the following rectangle.

Write and simplify an expression for the perimeter of the rectangle.

We are asked to write an algebraic expression for the perimeter of the given rectangle. Let's take a look at the figure.

The perimeter of a figure is the sum of all its side lengths. We are only given the length of two sides, but remember that a rectangle has two pairs of sides of equal length. Let's fill in the rest of the diagram.

We can multiply each both lengths by 2 and add the products to find the perimeter. Remember to use the Distributive Property.

The perimeter of the rectantle is 9z+2. We did it!

Simplify Algebraic Expressions

Catch-Up and Review

How Can These Terms Be Grouped?

Like Terms

Identifying Like Terms

Reducing the Number of Terms

Combining Like Terms

Heichi's Path to the Museum

Hint

Solution

Weekend Visitors to the Museum

Hint

Solution

A Curious Occurrence in the Souvenir Shop

Hint

Solution

Grouping Like Terms

Simplify Algebraic Expressions

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