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Lesson 3
The Distributive Property
State whether the equation is true or not with the
given values.
1.
6x – 4y = 22 when x = 5 and y = 2
2.
1
x
2
3.
y = – 3x – 1 when x = – 2 and y = – 7
+ 5 = y when x = 6 and y = 11
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.
1
( y  20)
4
1
1
( y )  (20)
4
4
1
y 5
4
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 ∙ 7
7(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 + 4y
2x + 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?