1. Expanding Algebraic Expressions

2. Focus Question
The value of an algebraic expression depends on the values of its variables. When you rewrite an algebraic expression in an equivalent form, you change how the expression looks, but you do not change its value.
When would you want to expand an algebraic expression? What operation would you use? What does expanding an expression help you do?

3. Examples Part 1
The algebraic expression 3 (x + 2) is a product with two factors.

4. Examples Part 1
You can use the Distributive Property to rewrite the product as the sum of two terms.

5. Examples Part 1

6. Examples Part 1
When you distribute negative numbers, be careful with the signs of the numbers.
EXAMPLE: -2 (-3y + 5)
Multiply each term inside the parentheses by -2.
EXAMPLE: -2 (-3y + 5) = -2 (-3y) + (-2)(5)
Use the Associative Property.
EXAMPLE: [-2 (-3)]y + -2(5) = 6y + (-10)
Write addition of a negative as subtraction.
EXAMPLE: 6y + (-10) = 6y - 10

7. Examples Part 1 Find an equivalent sum or difference for each product.
a(2 + b)
5(1 – 4c)
4(2 + x)
x(2 + x)

8. Key Concept
You expand an algebraic expression when you use the Distributive Property to rewrite a product as a sum or difference of terms.
Distribute FROM THE LEFT
EXAMPLE: 1.5 (2x + 3) = 1.5 (2x) + (1.5)(3)
= (1.5 · 2)x + 1.5(3)
= 3x + 4.5
Associative Property

9. Key Concept
You expand an algebraic expression when you use the Distributive Property to rewrite a product as a sum or difference of terms.
Distribute FROM THE RIGHT
EXAMPLE: (3a – b)5 = 3a · 5 – b · 5
= 3 · 5 · a – 5 · b
= 15a – 5b
Commutative Property
Associative Property

10. Key Concept
You expand an algebraic expression when you use the Distributive Property to rewrite a product as a sum or difference of terms.
Distribute A VARIABLE
EXAMPLE: y(2x – 3) = y(2x) – (y)(3)
= (2x)y – 3y
= 2xy – 3y
Commutative Property
Associative Property

11. Key Concept
You expand an algebraic expression when you use the Distributive Property to rewrite a product as a sum or difference of terms.
Distribute OVER THREE TERMS
EXAMPLE: 2 (3x – 9y + 2) = 2(3x) - 2(9y) + 2(2)
= ( 2 · 3)x - ( 2 · 9)y + 2(2)
= 6x – 18y + 4
Associative Property

12. Examples Part 2
Determine which three expressions can be expanded. Then expand.
7m + 7n 3x(2y) (6a – 10b)( 1 2 ) -4(x + 10y – 9) 3x(2 + y)
Which expression can be expanded? Write the expression in its expanded form.
(5 – x)(-y) (5 – x) - y

13. Examples Part 3
An architect draws plans for extending a rectangular deck.
Let x represent the increase, in meters, of the deck’s length.

14. Examples Part 3 Use the expression 3.7 (4.5 + x).
What does each factor of the expression represent? What does the expression represent?
Use the Distributive Property to expand the expression. What does each term of your new expression represent?

15. Close and Check
When would you want to expand an algebraic expression? What operation would you use? What does expanding an expression help you do?
Expanding an algebraic expression means using the Distributive Property to multiply each term of a sum by the same factor. Expanding an expression gives you a way to rewrite a product as a sum.

16. Distributive Property Practice worksheet
HW: