The Distributive Property

Lesson 3

State whether the equation is true or not with the given values.

1. 6x – 4y = 22 when x = 5 and y = 2

2. x + 5 = y when x = 6 and y = 11

3. y = – 3x – 1 when x = – 2 and y = – 7

2

1

Target: Simplify expressions using the Distributive

Property and combining like terms.

Term: A number or the product of a number and a variable.

Constant: Term that has no variable.

Coefficient: The number multiplied by a variable in a term.

Distributive Property: A property that can be used to rewrite an expression without parentheses.

Like Terms: Terms that have the same variable raised to the same power.

Equivalent Expressions: Expressions that have the same value.

For any numbers a, b and c:

a(b + c) = a ∙ b + a ∙ c

a(b – c) = a ∙ b – a ∙ c

Use the Distributive Property to simplify each expression.

2(x + 6)2(x) + 2(6)

2x + 12

Use the Distributive Property to simplify each expression.

)20(4

1y

)20(4

1)(

4

1y

54

1y

Use the Distributive Property to simplify each expression.

– 5(3x – 1)– 5(3x) – (– 5)(1)

– 15x + 5

Find the product by using the Distributive Property and mental math.

4(103)4(100 + 3)

4(100) + 4(3)400 + 12

412

Find the product by using the Distributive Property and mental math.

998 ∙ 77(1000 – 2)

7(1000) – 7(2)7000 – 14

6986

Find the product by using the Distributive Property and mental math.

8(6.5)8(6 + 0.5)

8(6) + 8(0.5)48 + 4

52

Simplify by combining like terms.

3x – 2y + 4 – 2x + x + 4y2x + 2y + 4

Simplify by combining like terms

– 5(2x – 1) + 3x – 2– 10x + 5 + 3x – 2

– 7x + 3

Simplify each expression.

1. 4(x − 3)

2. 9x + 2 + 3x – 4 − 7x

3. 10 + 8(2x + 3) − x

How could the Distributive Property help you do mental math in real-world situations?