Algebra I Block Name Unit #1: Linear Equations & Inequalities Period Lesson #2: Properties & Multiplying a Polynomial by a Monomial Date

Properties

In algebra, it is important to know certain properties. These properties are basically rules that allow us to manipulate and work with equations in order to solve for a given variable. We will be dealing with them all year, and you’ve probably actually been using them for awhile without even realizing it!

The Commutative Property deals with the order of things. In other words, if I switch the order of two or more items, will my answer be the same?

 The Commutative Property of Addition states that when it comes to adding two different numbers, the order does .  The Commutative Property of Multiplication states that when it comes to multiplying two different numbers, the order does .

When it comes to subtracting and dividing numbers, the order matter, so there are no commutative properties for subtraction or division.

The Associative Property deals with how things are grouped together. In other words, if I regroup two or more numbers, will my answer still be the same? Just like the commutative property, the associative property applies to addition and multiplication only.

There are Identity Properties that apply all four basic operations. When it comes to identity properties, just ask yourself “What can I do to keep the answer the same?”

 The identity property of addition states that if I add to anything, it will stay the same. The same is true for subtraction.  The identity property of multiplication states that if I multiply anything by ______, it will stay the same. The same is true for division.

One of the most important properties is the distributive property. The distributive property basically means you are going to multiply everything the parentheses by what is the parentheses.

Distributive Property Multiplying a polynomial by a monomial is rather easy- we just distribute the monomial over each term in the polynomial and write our answer in standard form. Give it a try….

REMINDER! When multiplying two of the same variable, you need to ADD the exponents. a.) 5(x2 – 3x + 11) b.) -3(x2 + 3x – 8)

c.) 2x(x2 – 4x + 5) d.) -3x(2x2 – 5x + 3)

e.) 2x2(x3 – 2x2 – 11) f.) -½ x2 (6x2 – 7x + 19)

Try these… 1.) 4(x2 – 5x + 2) 2.) 3(x2 + 5x – 11)

3.) -2(3x3 – 6x2 + 10x – 9) 4.) 5x(x2 – 3x + 2)

5.) -4x2(-2x2 + 8x – 17) 6.) -3x3(x2 + 8x – 11)

Write the letter of the property next to the equation that models that property.

7. 5 + x = x + 5 a. Identity Property of Multiplication

8. 6 + (x + 3) = (6 + x) + 3 b. Distributive Property

9. 5 ⋅ 1 = 5 c. Associative Property of Addition

10. 10 + 0 = 10 d. Commutative Property of Multiplication

11. 5(x2 – 2x + 7) = 5x2 – 10x + 35 e. Commutative Property of Addition

12. x – 0 = x f. Identity Property of Addition

13. 3 ⋅ 5 ⋅ 4 = 3 ⋅ 4 ⋅ 5 g. Identity Property of Subtraction

14.) A part of Jennifer’s work to solve the equation 2(6x2 – 3) = 11x2 – x is shown below.

Given: 2(6x2 – 3) = 11x2 – x Step 1: 12x2 – 6 = 11x2 – x

Which property justifies her first step?

(1) Identity property of multiplication (2) Multiplication property of equality (3) Commutative property of multiplication (4) Distributive property of multiplication over subtraction