Equivalent Expressions - DP, Factoring and CLT

​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

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 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

Distributive Property Steps

​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​