Simplifying Expressions with the Distributive Property

Objective: Simplify algebraic expressions involving distribution and combining like terms.

​Simplifying Expressions with the Distributive Property

​Distributive Property: a(b + c) = ab + ac

​ or a(b - c) = ab - ac

​Vocabulary

​Example 1

​4(x + 8)

​I know it starts off simple...

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​Here is a problem from the end of the lesson.

​Simplify: 4a - 3(b + 8) - a + 5b

Multiple Choice

Simplify: 5(y + 10)

• 5y + 50

• 5y + 10

• 5y + 15

• 5y + 5

EXAMPLE 2

Simplify: -3(x - 5)

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Math Response

Simplify: -9(x - 4)

Type answer here

Correct Answer: -9x+36

Deg^°

Rad

Match

Match the following each expression with what it would be AFTER you distribute.

• 6(x - 3)

• 6(x + 3)

• -6(x - 3)

• -6(x + 3)

6x - 18

6x + 18

-6x + 18

-6x - 18

• 6x - 18

• 6x + 18

• -6x + 18

• -6x - 18

EXAMPLE 3

Simplify: 3(4x - 2)

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Multiple Choice

Simplify: -4(2x - 5)

• -8x + 20

• -8x - 20

• -8x - 5

• -2x - 9

• -2x - 1

Math Response

Simplify: -6(3x - 9)

Type answer here

Correct Answer: -18x+54

Deg^°

Rad

Match

Match each expression with what it would be AFTER you distribute.

• 2(4x - 8)

• 2(4x + 8)

• -2(4x - 8)

• -2(4x + 8)

8x - 16

8x + 16

-8x + 16

-8x - 16

• 8x - 16

• 8x + 16

• -8x + 16

• -8x - 16

Simplifying Expressions

​Now we will distribute and then combine like terms

​Simplify: 3x + 2(x + 2) - 18

EXAMPLE 4

Multiple Choice

Simplify: 12 + 4(x - 5) + 7x

• 12 + 4x - 20 + 7x

• 11x - 8

• 11x + 7

• 3x - 8

Math Response

Simplify: -7 + 3(x - 8) - 8x + 3

Type answer here

Correct Answer: -5x-28

Deg^°

Rad

EXAMPLE 5

Simplify: 4a - 3(b + 8) - a + 5b

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Multiple Choice

Simplify: 3x + 2y + 4(x - 2y) + 7

• 7x - 6y + 7

• 7x + 7

• 7x + 10y + 7

• 17xy + 7

• 7x + 6y + 7

Math Response

Simplify: 2x - 6y + 3(2x - 5y) + 17

Type answer here

Correct Answer: 8x-21y+17

Deg^°

Rad