Number Properties

Identify

100

What property was used? 3+2+7=2+3+7

The Commutative Property of Addition.

200

Are these equivalent expressions? 3x+6(4x+5)=27x+35

Not equivalent.

300

What property was used? (3x6)x7x6=(3x6)x(7x6)

The Associative Property of Multiplication.

400

What property was used? 75+15=5(15+3)

The Distributive Property

500

What property was used? (3+x)(2+17)=(2+17)(3+x)

The Commutative Property of Multiplication.

Rewritten

100

Use the Commutative Property to rewrite the expression ____+___=32+14

14+32

200

Use the Associative Property to rewrite the expression (x+5)+3=

x+(5+3)

300

Use the Distributive Property to rewrite the expression. 30+25

5(6+5)

400

Use the Associative Property to rewrite the expression 7x(9x8)x5

(7x9)x8x5 or 7x9x(8x5)

500

Use the Commutative Property of Addition to rewrite the expression (4x3)+(5x10)

(5x10)+(4x3)

Simplify

100

2(x+5)

2x+10

200

7(2x-8)

14x-56

300

5(x+4)+3x+3

8x+23

400

3+2x+4(x+6)

6x+27

500

x(10+20)-24x+5

6x+5

Definitions

100

a(b+c)=ab+ac

What is the Distributive Property.

200

a+b+c=b+c+a

What is the Commutative Property of Addition.

300

(a+b)+c=a+(b+c)

What is the Associative Property of Addition.

400

abc=cba

What is the Commutative Property of Multiplication.

500

(ab)cd=a(bc)d

What is Associative Property of Multiplication

Polynomials

100

7xy² + 14x⁴y - 28xy

What is 7xy(y + 2x³ - 4)

200

2y² - 2z - ay² + az

What is (2-a)(y²-z)

300

x² - 17x + 72

What is (x-8)(x-9)

400

x² - 36y⁴

What is (x-6y²)(x+6y²)

500

10(2a-1)² - 19(2a-1) - 15

What is 2(5a - 1)(4a - 7)