Expressions-Operations

Combining Like Terms

Day 1

Vocab Review

Let's review some terms that we will be using in the classroom :)

Expression

An expression contains numbers, variables, and operation symbols...NO EQUAL SIGN

Multiple Select

Which of these can be found in an expression?

• Numbers

• Operations

• Equal Sign

• Variables

Terms

Multiple Choice

The following expression contains how many terms?

$$-3x+y-2-5x$$  

• 2

• 3

• 4

• 5

Variable

A letter that stands for an unknown number.

VARIABLE TERM refers to the entire term that contains the variable (Ex: -8x)

When there is no number in front of the variable, there is a 1 there. (Ex: y is the same as 1y)

Multiple Select

In the following expression, what are the variable terms:

$$2x-3+6y-1$$  

• 2x

• -3

• 6y

• -1

Coefficient

Multiple Select

Which of the following are coefficients in this problem?

$$-2-5a+1-6b^2$$  

• -2

• -5

• 1

• -6

Constant

A number NOT connected to a variable.

Always include the sign before it .

Constants can be whole numbers, decimals, or fractions.

All constants are like-terms!

Multiple Select

What are the constants in the following problem?

$$2b^2+1-6a+4.2$$  

• 2

• 1

• -6

• 4.2

Like-Terms

Multiple Select

Which of the following are examples of like-terms?

• $$3b\ \&\ b$$

• $$6x^2\ \&\ 6x$$

• $$3\ \&\ 4.5$$

• $$6xy\ \&\ 6x^2y$$

Combining Like Terms

Use the signs in front of the terms.

Only terms that share the same variable (raised to the same power) can be combined.

Always ADD the terms together but remember to look at the signs before it!

Multiple Choice

Simplify this expression by combining the like-terms:

$$2x+7-4x$$  

• $$5x$$  

• $$-2x$$  

• $$-2x+7$$  

• $$-13x$$  

Multiple Choice

Simplify the expression by combining like-terms:

$$-3y+1+9y-4$$  

• $$3y$$  

• $$6y-3$$  

• $$12y+3$$  

Multiple Choice

Simplify the expression by combining like-terms:

$$b+3b+7$$  

• $$3b^2+7$$  

• $$3b+7$$  

• $$4b+7$$  

Using the Distributive Property

To distribute, multiply the number on the outside of the parentheses by all terms inside the parentheses. Remember to be careful of the signs!

Multiple Choice

Use the Distributive Property.

3(x + 9)

• 3x + 9

• 3x + 12

• 3x + 27

• x + 27

Multiple Choice

Use the Distributive Property.

-4(2x - 6)

• -6x - 6

• -6x + 24

• -8x - 6

• -8x + 24

What step would I take next to simplify this expression?

Multiple Select

What step would I take next to simplify the expression from the previous question?

• combine like terms

• distribute again

• there is nothing to do further, that is your answer

• switch the signs to their opposite

Simplifying Expressions

• Apply the Distributive Property

• Combine Like Terms

Multiple Select

Simplify the Expression:

2(x - 4) + 5x

• 5x - 6

• 7x - 8

• 3x - 4

• 7x - 4

Multiple Choice

I can apply the distributive property to an expression.

$$2\left(3x+4\right)=$$  

• $$14x$$  

• $$6x+8$$  

• $$6x+4$$  

Multiple Choice

I can apply the distributive property to an expression.

$$2\left(3x-4\right)=$$  

• $$-2x$$  

• $$6x+8$$  

• $$6x-8$$  

Multiple Choice

I can apply the distributive property to an expression.

$$-2\left(3x-4\right)=$$  

• $$-6x-4$$  

• $$-6x+8$$  

• $$6x+8$$  

Equivalent Expressions

Multiple Choice

Which answer choice is equivalent to:
5(2x-3)-3x

• 10x-6
• 7x-15
• 6-10x
• 15-7x

Multiple Choice

Which expression is equivalent to 7(3a + 4b)?

• 21a + 28b
• 10a + 11b
• 21a + 4b
• 10a + 28b

Multiple Choice

Which expression is equivalent to 3a² + 6a + 5a²?

• 14a²
• 14a
• 8a² + 6a
• 3a² + 11a

Multiple Choice

Which expression is equivalent to 3x + 5 + 7x + 2?

• 10x + 7
• 17x
• 17
• 15x + 2

Multiple Select

Which answer choice is equivalent to:

12x-16

Select all that apply.

• 3(4x+5)

• 3(4x-6)

• 4(4x-3)

• 4(3x-4)

• 8x-(4⋅4)+4x

Multiple Choice

Find an equivalent expression for the given expression: 36x + 24

• 4(9x + 7)
• 4(9x + 8)
• 2(18x + 12)
• 12(3x + 3)

Multiple Choice

Find an equivalent expression for the given expression: 36x + 24

• 4(9x + 7)
• 4(9x + 8)
• 2(18x + 12)
• 12(3x + 3)

Multiple Choice

Use the distributive property to find an equivalent expression: 5(2f + 4)

• 10f + 4
• 10f + 9
• 10f + 20
• 30f

Adding Linear Expressions

• Get rid of the parentheses

• Combine like terms

• We can do this because the plus sign in between the sums when distributed keeps all the signs the same

Multiple Choice

Simplify by adding these linear expressions: (9x + 7) + (x + 3)

• 10x + 10

• -10x - 10

Multiple Choice

Add the linear expressions:

(3x + 7) + (10x -3)

• 13x + 10

• 13x + 4

Multiple Choice

Simplify: (6p + 4) + (-5p + 8)

• -30p + 48

• p + 12

Multiple Choice

Simplify: (5x - 1) + (3x + 6)

• -15x + 10

• 8x + 5

Open Ended

Try it:

$$\left(10x-1\right)-\left(3x+2\right)$$  

Practice:

Open Ended

Try it:

$$\left(12x+2\right)-\left(-3x-1\right)$$  

Larger Expressions

Open Ended

Try It:

$$\left(2x+3xy-8y\right)-\left(x+10y-2xy\right)$$  

How to FACTOR by "undoing" Distributive Property

14x + 35

What is the GCF of each term?


THE GCF is 7
7 (__ + __)

So now

7 (2x + 5)

because 7 x 2x =14x AND 7x 5 =25

Multiple Choice

Factor

9x - 72

• 3x(3-9)

• 9x(-8)

• 3(3x-9)

• 9(x-8)

Multiple Choice

Factor

9x+12

• 9(x-3)

• 3(3x+4)

• 3x(3+4)

• 3(3x-4)

Multiple Choice

Factor

16x - 20

• 4(4x - 5)

• 2x(8-10)

• 4x(4-5)

• 2(8x-10)