Equivalent Expressions - DP, Factoring and CLT

​Distributive Property

and

Like Terms​

​

​Simplifying

Expressions​

​Vocabulary to Know

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​Parts of an expression see graphic

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Like Terms​ same variable, same power

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Terms everything but a + sign

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Distributive Property A (B + C) can be solved as A (B + C) = AB + AC.

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Simplify​ expression with no like terms and no parenthesis

​Simplifying Expressions

involves​

​In 7th Grade, Like Terms and Distributive Property may include fractions and negative values.

​Combining

Like Terms

​Distributive Property

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​Like Terms

​Like Terms have the EXACT same variables and same exponents.

Like Terms

2x, -5x

-8, 10

3y², 8y²

7xy, -xy​

All constants are like terms ​1, -5, 1/2, -0.75 are all Like Terms

Unlike Terms

4x, 4y

9, 6x​

-5x, 5x²

3x²y, 8xy²

​Example

Find the Like Terms​

7x, ​-8, 4y, x, x², 6, 5xy, 8y, 9

7th Grade Math

​Unit 2

​Example Solution

Find the Like Terms​

7x, ​-8, 4y, x, x², 6, 5xy, 8y, 9

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9 terms​

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7th Grade Math

​Unit 2

Term Types​

x x² y xy Values​

7x x2 4y 5xy -8​

x 8y 6

9​

Terms must be ​Like Terms in order to add or subtract them.

To Combine Like Terms

1. Add the Coefficient

2. Keep the variable​

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​You may color code like terms.

​Combining Like Terms

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Great property to use when you cannot compute inside the grouping symbols because the terms are unlike. ​

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​Some text here about the topic of discussion.

​Distributive Property

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​Distributive Property TIP

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​Prior to distributing the factor to each term, combine any like terms that are inside the ( ).

In this case, 2a and 3a were combined to make 5a before ​multiplying the terms by 4.

3 EQUIVALENT Expressions

It is typical to use arrows to show the outside value ​being multiplied by each term inside the ( ).

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It is important to recognize that 2(x) + 2(1) is an equivalent expression as well as 2x + 2.

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Spend the extra second to write this step so you can improve the skill of identifying equivalent expressions. ​

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​2(x+1) = 2(x) + 2(1) = 2x + 2

​Distributive Property TIP

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​Do not skip this step

​Beginning

written as factors​

​Distributing factor to both terms

aka mama's love​

​Multiply

​Ending

Written as sum

Simplified ​

IF NEEDED

Rewritten as difference to Eliminate the awkward + -​

Distributive Property Steps

​Simplifying Expressions

​A Simplified Expression has

No Like Terms and

No Parenthesis.

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​To Simplify an Expressions

​ 1. Notice Negatives,

aka use Additive Inverse Property

aka Keep, Change, Change (KCC)

2. Distribute factors if any

   aka ​mama's love

3. Combine Like Terms​

Multiple Choice

2(c - 8)

• 2c - 16

• 2c + 16

• 2c - 8

• c - 16

Multiple Choice

Which of these are like terms in the following expression:
3x + 7 - 9x + 24y + 2x²

• 7, 24y

• 3x, 9x

• 3x, -9x

• 3x, -9x, 2x²

Multiple Choice

Evaluate the expression 6z - 2t when z = 4 and t=3

• 41
• 1
• 12
• 18

Multiple Choice

What is the coefficient in the expression: 94abc?

• 9
• 4
• 94
• abc

Multiple Choice

Simplify by combining like terms:
5a + 2b - 3a + 4

• 8a + 2b + 4
• 2a + 2b + 4
• 8ab
• 4ab + 4

Multiple Choice

Write an expression to show 6 less than x.

• x - 6
• x⁶
• x ÷ 6
• 6 - x

Multiple Choice

Write an expression to show the product of h and g.

• hg
• h + g
• h - g
• h ÷ g

Multiple Choice

Which expression is equivalent to: -3 - (2.5 - 4)

• -3 + 2.5 - 4
• -3 + -2.5 - 4
• -3 - -2.5 - -4
• -3 + -2.5 - -4

Multiple Choice

Which expression is equivalent to: 8 - (-7 + 6)

• 8 + 7 + 6
• 8 + 7 - 6
• 8 - - 7 + 6
• 8 - 7 - 6

Multiple Choice

Which of the following is NOT equivalent to: 
-5 - (3 + 9)

• -5 - 3 + 9
• -5 + -3 - 9
• -5 - 3 - 9
• -5 - 3 + -9

Multiple Choice

The width of a rectangle is 8x - 1 ft. and the length is 3x + 9 ft. Find the perimeter of the rectangle

• 22x + 16
• 5x - 10
• 19x
• 11x + 8

Multiple Choice

Which of the following is NOT equivalent to 42x + 24?

• 2(21x + 12)
• 3(14x + 8)
• 6(7x + 4)
• 7(6x + 17)

Multiple Choice

Find the Sum: 
(5 - t) + (3t +2)

• 2t + 7
• 2t + 3
• -2t + 3
• -2t + 7

Multiple Choice

Find the difference:
(8 - u) - (5u + 1)

• 6u + 7 
• -4u + 7
• -6u + 7
• 4u - 7

Multiple Choice

Find the difference: 
2(x - 2) - 3(x - 4)

• -x - 8
• x + 8
• 5x + 8
• -x + 8

Multiple Choice

Find the difference:
(2x + 7) - 3(5x - 4)

• -13x - 5
• 17x + 5
• 17x + 5
• -13x + 19

Multiple Choice

(x + 9y + 5) – (-8x + 4y – 7)

• -7x + 5y + 12
• 9x + 9y + 12
• -7x + 13y + 12
• 9x + 5y + 12

Multiple Choice

(6x + 3y + 4) – (x + y – 5)

• 5x + 2y + 9
• 7x + 2y + 9
• 7x + 4y + 9
• 5x + 2y -1

Multiple Choice

A local bookstore is advertising $3 off the price of each book. You decide to buy 6 books. Let p represent the price of each book. Use the expression 6(p – 3). 
Which of the following is equivalent to  the expression?

• p - 18

• 6p - 18

• 6p - 63

• p - 3

Multiple Choice

Find an equivalent expression -(5x + 1)? Careful with the negative.

• -5x + 1
• -5x - 1
• 5x + 1
• 5x - 1

Multiple Choice

Which of the following is equivalent to 8(5f - 7) + 3f ?

• 43f - 7
• -13f
• 43f - 56
• 40f -7 + 3f