You can use algebra tiles to model algebraic expressions.

1
MODELING THE DISTRIBUTIVE PROPERTY
You can use algebra tiles to model algebraic
expressions.
1-tile
x-tile
1
1
1
x
This 1-by-1 square tile has an area of 1 square
unit.
This 1-by-x square tile has an area of x
square units.
Model the Distributive Property using Algebra
Tiles

Area 3(x 2)
Area 3(x ) 3(2)
2
The product of a and (b c)


a(b c) ab ac
2(x 5)
2(x) 2(5)
2x 10


(b c)a ba ca
(x 5)2
(x)2 (5)2
2x 10


y(1 y)
y(1) y(y)
y y 2


(1 5x)2
(1)2 (5x)2
2 10x
3
Remember that a factor must multiply each term of
an expression.
Distribute the 3.
(3)(1 x)
(3)(1) (3)(x)
Simplify.
3 3x
Distribute the 2.
(y 5)(2)
(y)(2) (5)(2)
Simplify.
2y 10
a 1 a
(7 3x)
(1)(7) (1)(3x)
Simplify.
7 3x
Forgetting to distribute the negative sign when
multiplying by a negative factor is a common
error.
4
SOLUTION
You are shopping for CDs. You want to buy six CDs
for 11.95 each.
The mental math is easier if you think of 11.95
as 12.00 .05.
Write 11.95 as a difference.
6(11.95) 6(12 0.05)
6(12) 6(0.05)
Use the distributive property.
Use the distributive property to calculate the
total cost mentally.
72 0.30
Find the products mentally.
71.70
Find the difference mentally.
5
SIMPLIFYING BY COMBINING LIKE TERMS
Each of these terms is the product of a number
and a variable.
Like terms have the same variable raised to the
same power.
y2 x2 3y3 5 3 3x2 4y3 y
6
(8 3)x
8x 3x
Use the distributive property.
11x
Add coefficients.
4x2 2 x2
4x2 x2 2
Group like terms.
3x2 2
Combine like terms.
3 2(4 x)
3 (2)(4 x)
Rewrite as addition expression.
3 (2)(4) (2)(x)
Distribute the 2.
3 (8) (2x)
Multiply.
5 (2x)
Combine like terms and simplify.
5 2x