1. The Distributive Property
Section 1-7 Part 1

2. Goals
Goal
Rubric
To use the Distributive Property to simplify expressions.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary
Distributive Property

4. Distributive Property
To solve problems in mathematics, it is often useful to rewrite expressions in simpler form.
The Distributive Property, illustrated by the area model on the next slide, is another property of real numbers that helps you to simplify expressions.

5. MODELING THE DISTRIBUTIVE PROPERTY
You can use algebra tiles to model algebraic expressions. 1
1-tile 1
x-tile 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 3 3 x 3 2
x + 2 +
x + 2
Area = 3(x + 2)
Area = 3(x ) + 3(2)

6. Distributive Property
The Distributive Property is used with Addition to Simplify Expressions.
The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

7. USING THE DISTRIBUTIVE PROPERTY
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

8. The Distributive Property
For any numbers a, b, and c,
a(b + c) = ab + ac and (b + c)a = ba + bc;
a(b - c) = ab - ac and (b - c)a = ba - bc;
Distributive Property
The mailman property
Find the sum (add) or difference (subtract) of the distributed products.

9. USING THE DISTRIBUTIVE PROPERTY
Remember that a factor must multiply each term of an expression.
(–3)(1 + x)
= (–3)(1) + (–3)(x)
Distribute the –3.
Simplify.
= –3 – 3x
(y – 5)(–2)
= (y)(–2) + (–5)(–2)
Distribute the –2.
Simplify.
= –2y + 10
–(7 – 3x)
= (–1)(7) + (–1)(–3x)
–a = –1 • a
Simplify.
= –7 + 3x
Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

10. Your Turn: Simplify 1) 4) 2) 5) 3) 6)

11. Your turn: 2(x + 5) = 5. (x - 4)x = (15+6x) x = 6. y(2 - 6y) =

12. Joke Time What’s green and has wheels? Grass… I lied about the wheels.
Why did the squirrel fall out of the tree?
Because it was dead.
What do you call a fly with no wings?
A walk.

13. Assignment
1.7 Pt 1 Exercises Pg. 54 – 55: #4 – 40 even