Structures of Expressions Unit Test Review

Addition of Polynomials

100

(4x² + 2x) + (x² + 6x)

5x² +8x

200

(-3y² + y) + (4y² + 6y)

y² +7y

300

(2a² - 7a + 10) + (a² + 4a + 7)

3a² -3a +17

400

(2r² - 5r + 7) + (3r³ - 6r)

3r³ + 2r² -11r + 7

500

(5r³ - 6r² +3r) + (r² -2r - 3)

5r³ - 5r² + r - 3

Subtraction of Polynomials

100

(y² - 10xy) - (2y² + 3xy)

-y² -13xy

200

(2x² + 5x - 3) - (3x³ + 2x - 5)

-3x³ + 2x² +3x + 2

300

(-3a² - 2a) - (4a² - 4)

-7a² - 2a + 4

400

(4x³ + 5x + 2) - (1 + 2x - 3x²)

4x³ + 3x² +3x + 1

500

(4 - x - 2x²) - (-2 + 3x - x³)

x³ - 2x² - 4x + 6

Multiply Monomials

100

(6x²)(5x)

30x³

200

2x(x + 6) 

2x² + 12x 

300

(4m + 2)(4m + 5)

16m² + 28m + 10

400

(a + 3)(a − 2)

a² + 1a − 6

500

(x - 2)²

x² - 4x + 4 

Associative, commutative and Distributive

100

Which property allows you to change where the parentheses are? 

Associative Property

200

Which property allows you to change the order? 

Communative Property 

300

Simplify the expression using the distributive property:

2(x² - 4x + 7)

2x² - 8x + 14

400

Are the following two expressions equivalent?  How do you know?

Expression 1: (x + 2) + (3x + 4)

Expression 2: 4x + 6

These are equivalent by the associative property of addition.

500

Are the following two expressions equivalent?  How do you know?

Expression 1: 7x + 2 - 3x + 11

Expression 2: x² + 4x + 13 - x²

Expression 1: 4x + 13

Expression 2: 4x + 13

We know these are equivalent by the commutative property of addition.

Mixed Review

100

(3x² + 4x -1) + (x² - 2x + 8)

4x² + 2x + 7

200

(5x² + 6x + 13) - (2x² + 8 )

3x² + 6x + 5

300

Are the following two expressions equivalent?  How do you know?

Expression 1: (3x + 7) - (6x + 4)

Expression 2: -3x + 3

These are equivalent by the associative property of addition.

400

(2x² + 5)(x - 2)

2x³ - 4x² + 5x - 10

500

Are the following two expressions equivalent?  How do you know?

Expression 1: 8x + 2 + x - 7

Expression 2: 4x + 3x - 5 + 2x

Expression 1: 9x - 5

Expression 2: 9x - 5

These two expressions are equivalent by the commutative property of addition.