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Algebra 1

Simplify Expressions Using the Distributive Property: Mini-Lesson Review

Algebra 1Simplify Expressions Using the Distributive Property: Mini-Lesson Review

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Mini Lesson Question

Question #2: Simplify Expressions Using the Distributive Property

Which expression is equivalent to 2 ( x 4 )
  1. 2 x 8
  2. 2 x + 8
  3. 2 x 8
  4. 2 x 4

Simplify Expressions Using the Distributive Property

The Distributive Property can be used to remove parentheses as you simplify expressions.

DISTRIBUTIVE PROPERTY

If a , b , c are real numbers, then a ( b + c ) = a b + a c Also, ( b + c ) a = b a + c a a ( b c ) = a b a c ( b c ) a = b a c a If a , b , c are real numbers, then a ( b + c ) = a b + a c Also, ( b + c ) a = b a + c a a ( b c ) = a b a c ( b c ) a = b a c a

Simplify:

1. 3 ( x + 4 ) 3 ( x + 4 )

It may help to use arrows to show the Distributive Property.

The image shows the expression 3(x + 4) with curved arrows pointing from the 3 to both the x and the 4 inside the parentheses, indicating distribution.

Use the Distributive Property.

3x+34 3x+34

Multiply.

3 x + 12 3 x + 12

2. 11 ( 4 3 a ) 11 ( 4 3 a )

Use arrows to show the Distributive Property.

The expression -11(4 - 3a) with one arrow curving from -11 to 4, and another from -11 to -3a, indicating distribution of -11 to both terms inside the parentheses.

Use the Distributive Property

-114- (-11) 3a -114- (-11) 3a

Multiply.

-44-(-33a) -44-(-33a)

Simplify.

-44+33a -44+33a

Watch signs when using the Distributive Property with negative signs.

Try it

Try It: Simplify Expressions Using the Distributive Property

Simplify: 2 ( 4 y + 1 ) 2 ( 4 y + 1 ) .

Check Your Understanding

Which expression is equivalent to 4 ( 5 2 a ) 4 ( 5 2 a ) ?

Multiple Choice:

  1. 20 2 a 20 2 a

  2. 20 + 2 a 20 + 2 a

  3. 20 8 a 20 8 a

  4. 20 + 8 a 20 + 8 a

Videos: Using the Distributive Property to Simplify Expressions

Watch the first 2 minutes and 40 seconds of the video to see how to use the Distributive Property to simplify expressions.

Khan Academy: Distributive property with variables

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