7.EE.A.1 Expand and Factor Linear Equations

Expand and Factor Linear Equations

Standard 7.EE.A.1

PEMDAS

Using the Order of Operations to solve mathematical equations.

PEMDAS

• Parenthesis

• Exponents

• Multiplication/Division (in the order they are seen in the problem)

• Addition/Subtraction (in the order they are seen in the problem)

Using PARENTHESIS

• ALWAYS work the parenthesis first in a math equation.

• EXAMPLE

• 45+(20-5)

• 20-5 is done FIRST because it is in the parenthesis THEN the rest of the problem is worked.

• The answer would be 30

Multiple Choice

SOLVE THE PARENTHESIS FIRST

55+(20-5)=

What do the PARENTHESIS "break down" to?

• 5

• 40

• 15

• 70

Multiple Choice

SOLVE THE PARENTHESIS FIRST

29+(18-2)

WHAT DO THE PARENTHESIS BREAK DOWN TO?

• 45

• 16

• 20

• 14

Distributive Property

Remember that multiplication is just REPEATED ADDITION!

Multiple Choice

5(a + 6)

• 5a + 6

• a + 30

• 5a + 30

• 5a - 30

Multiple Choice

Which of the following is equivalent to 4(2x + 3)

• 8x + 12
• 8x + 3
• 8x - 12
• 20x

Multiple Choice

What do the parentheses tell you to do?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

3(3x +1)

• 9x +3
• 3x + 3
• 12x
• 9x + 1

Multiple Choice

6 (x + y + 7)

• 6x + 6y + 42

• 12xy + 42

• 6x + 6y + 7

• 6x6y + 42

Multiple Choice

Distribute

9(x - 5)

• 9x - 45

• 9x + 5

• 9x + 14

• 9x + 45

Multiple Choice

Distribute
-15( 2x - 2)

• -15 + 2x + 2
• -30x + 30
• -30x - 30
• -15x + 2

Multiple Choice

Use the distributive property to write an equivalent expression.
-8(z - 5)

• -8z - 40
• -8z + 40
• -8z - 13
• -8z - 13

Multiple Choice

3(2c - 5)

• 6c - 15
• 6c + 15
• 6c + 15
• -6c - 15

Multiple Choice

  $$7\left(5x-1\right)$$  

• $$35x+7$$  

• $$35x-1$$  

• $$35x-7$$  

• $$-35x-7$$  

Multiple Choice

(x - 6)4

• 24 - 4x
• 4x - 6
• x - 24
• 4x - 24

Multiple Choice

(b + 8)5

• b + 40
• 5b - 40
• 5b + 40
• 5b + 8

Simplifying Expressions & Solving Equations

Multiple Choice

Which expression is equivalent to the expression $$-3\left(4x-2\right)-2x?$$  

• $$-8x$$  

• $$-16x$$  

• $$-14x-2$$  

• $$-14x+6$$  

Multiple Choice

Which expression is equivalent to $$7a-8-12a+4?$$  

• $$-9a$$  

• $$31a$$  

• $$-5a-4$$  

• $$19a+12$$  

Multiple Choice

Expand using the distributive property

-2(3x + 4y + 1)

• -6x + 8y + 2

• -6x - 8y + 2

• -6x - 8y - 1

• -6x - 8y - 2

Multiple Choice

Simplify the expression (this means distribute and/or combine like terms):

• 20 = 38 + 3x

• 20 = 17x + 24

Multiple Choice

Do I need to distribute, combine like terms, or both?

• Distribute

• Combine like terms

• Both

Simplifying Expressions with Like Terms

Objective: Simplify algebraic expressions by combining like terms.

​Like Terms: terms that have the SAME variable(s)

​

​Example: 4x and 17x

​

​Unlike Terms: terms that DO NOT have the same variable(s)

​

​Example: 4x and 17xy

​Vocabulary

Match

Match the following like terms.

• 8x

• 12x²

• 4x²y

• 7xy²

• 9y

-x

6x²

-9x²y

2xy²

-12y

• -x

• 6x²

• -9x²y

• 2xy²

• -12y

​Combine Like Terms: take multiple like terms and make them one

​

​Another word used is SIMPLIFY.

​Vocabulary

​Example 1

​Simplify: 4x - 9x + 10x

Match

Match the following expressions with their simplified form after you combine like terms.

• 8x - 9x

• -8x + 9x

• -8x - 9x

• 8x - (-9x)

-x

x

-17x

17x

• -x

• x

• -17x

• 17x

​Example 2

​Simplify: 10 - 4ab + 2 + 8ab

Multiple Choice

Rewrite the expression by combining like terms.

8y² + 7xy – 2y² - 5xy + 2x

• 10y² + 2xy + 2x

• 6y² + 2xy + 2x

• 6y² + 12xy + 2x

• 10y² + 12xy + 2x

Math Response

Simplify: 5x + 3x + 4 + 7y

Type answer here

Correct Answer: 8x+7y+4

Deg^°

Rad

Multiple Select

Choose the expressions that can be simplified.

• 12x² - 4x + 1

• -4x + 9xy - 10

• 13x - 9 - x

• 8y - 2x + 4y - 9x

• 7y² - 7xy + 9y

Math Response

Simplify: 12y + 9x - 4 - 6x + 4y

Type answer here

Correct Answer: 3x+16y-4

Deg^°

Rad