Master Simplifying Algebraic Expressions: Practice Quiz for College Algebra

Question 1

Use the distributive property to simplify the expression: 4(x - 3)

Accepted Answer

4x - 12

Answer

x - 12

Answer

4x + 12

Answer

x + 12

Question 2

Factor the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)(x - 3)

Answer

(x - 9)(x + 1)

Answer

(x + 9)(x - 1)

Question 3

Simplify the expression: (3x^2y)^2

Accepted Answer

9x^4y^2

Answer

x^4y^2

Answer

9x^3y^4

Answer

x^3y^4

Question 4

Factor the expression: x^3 - 27

Accepted Answer

(x - 3)(x^2 + 3x + 9)

Answer

(x + 3)(x^2 - 3x + 9)

Answer

(x - 9)(x^2 + 9x + 81)

Answer

(x + 9)(x^2 - 9x + 81)

Question 5

What is the factored form of the expression x² - 9?

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

x² - 3x + 3

Answer

Cannot be factored

Question 6

Simplify the following expression: (x - 2)^3

Accepted Answer

x^3 - 8x^2 + 24x - 16

Answer

x^3 - 6x^2 + 12x - 8

Answer

x^3 + 8x^2 + 24x + 16

Answer

x^3 + 6x^2 + 12x + 8

Question 7

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Answer

(x - 3)^2

Question 8

Simplify the following expression: (2x + 3)^2 - (2x - 3)^2

Accepted Answer

0

Answer

4x

Answer

12x

Answer

16x

Question 9

Use the distributive property to simplify the expression: **3(x + 2)**

Accepted Answer

3x + 6

Answer

6x + 2

Answer

3x - 6

Answer

6x - 2

Question 10

Factor the following expression: **x^2 - 4**

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(x - 2)^2

Answer

(x + 4)^2

Question 11

Which of the following is equivalent to the expression: **2x^2y - 6xy^2**?

Accepted Answer

2xy(x - 3y)

Answer

xy(2x - 6y)

Answer

x(2xy - 6y^2)

Answer

y(2x^2 - 6xy)

Question 12

Which of the following is the perimeter of the rectangle with length (x + 3) and width (x - 2)?

Accepted Answer

2x + 6

Answer

2x - 6

Answer

4x + 2

Answer

4x - 2

Question 13

Which of the following is the area of the triangle with base (2x - 1) and height (x + 3)?

Accepted Answer

x^2 + 5x - 3

Answer

x^2 - 5x - 3

Answer

2x^2 + 5x - 3

Answer

2x^2 - 5x - 3

Question 14

Simplify the expression: **(sqrt(x) + 3)^2**

Accepted Answer

x + 6sqrt(x) + 9

Answer

x - 6sqrt(x) + 9

Answer

x + 9sqrt(x) + 9

Answer

x - 9sqrt(x) + 9

Question 15

Use the distributive property to simplify the expression: 3(x + 2)

Accepted Answer

3x + 6

Answer

3x - 2

Answer

x + 6

Answer

6x + 2

Question 16

Which of the following is NOT a step in simplifying algebraic expressions?

Accepted Answer

Multiplying exponents

Answer

Combining like terms

Answer

Applying the distributive property

Answer

Factoring

Question 17

Simplify the following expression: (x - 2)²

Accepted Answer

x² - 4x + 4

Answer

x² - 4

Answer

x² + 4

Answer

x² + 4x + 4

Question 18

Apply the distributive property to simplify the expression: 2(x - 3).

Accepted Answer

2x - 6

Answer

x - 6

Answer

2x + 6

Answer

x + 6

Question 19

Simplify the following algebraic expression by combining like terms: (2x^2y - 3xy^2) + (x^2y + 5xy^2).

Accepted Answer

3x^2y + 2xy^2

Answer

3x^2y - 8xy^2

Answer

x^2y + 8xy^2

Answer

x^2y - 2xy^2

Question 20

Simplify the following expression: (x + 2)(x - 3) - (x - 1)(x + 4).

Accepted Answer

x^2 - 5x - 10

Answer

x^2 + 5x - 10

Answer

-x^2 + 5x + 10

Answer

-x^2 - 5x - 10

Question 21

Simplify the radical expression by rationalizing the denominator: sqrt((x + 2)^2).

Accepted Answer

x + 2

Answer

x - 2

Answer

|x + 2|

Answer

|x - 2|

Question 22

Use the distributive property to simplify: 2(x + 3)

Accepted Answer

2x + 6

Answer

2x + 3

Answer

x + 6

Answer

x + 9

Question 23

Which of the following is NOT a method for simplifying algebraic expressions?

Accepted Answer

Dividing both sides by a constant

Answer

Combining like terms

Answer

Applying the distributive property

Answer

Factoring

Question 24

Which of the following expressions is equivalent to 2(x^2 - 3x + 2)?

Accepted Answer

2x^2 - 6x + 4

Answer

4x^2 - 6x + 8

Answer

2x^2 - 6x + 2

Answer

4x^2 - 3x + 4

Question 25

Simplify the expression: (x - 2)^2

Accepted Answer

x^2 - 4x + 4

Answer

x^2 - 4

Answer

x^2 + 4

Answer

x^2 + 4x + 4

Question 26

Factor the polynomial: x^3 - 8

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 2)(x^2 + 4)

Answer

(x + 2)(x^2 - 4)

Question 27

Simplify the algebraic expression: 3x + 2y + x - 5y

Accepted Answer

4x - 3y

Answer

2x + 3y

Answer

5x - 3y

Answer

x - 3y

Question 28

Simplify the algebraic expression: (3x^2 - 2x + 1) - (x^2 + 5x - 3)

Accepted Answer

2x^2 - 7x + 4

Answer

-x^2 - 7x + 4

Answer

x^2 - 7x + 4

Answer

2x^2 + 7x - 4

Question 29

Simplify the rational expression: (x - 2)(x + 3) / (x - 2)

Accepted Answer

x + 3

Answer

(x - 2)(x + 3)

Answer

x^2 + 3

Answer

x - 3

Question 30

Combine and simplify the rational expressions: 1 / (x - 2) - 1 / (x + 2)

Accepted Answer

-4 / (x^2 - 4)

Answer

-2 / (x + 2)

Answer

2 / (x - 2)

Answer

4 / (x^2 - 4)

Question 31

Simplify the radical expression: sqrt(16x^2y^4)

Accepted Answer

4xy^2

Answer

2xy^2

Answer

8xy^2

Answer

16xy^4

Question 32

Perform polynomial division to simplify the expression: (x^2 + 2x + 1) / (x + 1)

Accepted Answer

x + 1

Answer

x^2 - 1

Answer

(x + 1)^2

Answer

x - 1

Question 33

Simplify the expression involving fractional exponents: (2x^3 - 4x^2 + 6x) / 2x

Accepted Answer

x^2 - 2x + 3

Answer

x^2 + 2x + 3

Answer

x^3 - 2x^2 + 3x

Answer

x^2 - 2x - 3

Question 34

Simplify the expression: 2x + 3y - x + 5y

Accepted Answer

x + 8y

Answer

-x + 2y

Answer

8x + 2y

Answer

x - 2y

Question 35

Simplify the expression: (x - 2)(x + 3)

Accepted Answer

x^2 + x - 6

Answer

2x^2 - x - 6

Answer

x^2 - x - 6

Answer

2x^2 + x - 6

Question 36

Factor the expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 9)

Answer

(x - 3)^2

Answer

(x + 3)^2

Question 37

Simplify the expression: (x^2 - 1) / (x - 1)

Accepted Answer

x + 1

Answer

x^2 - 1

Answer

x - 1

Answer

x^2 + 1

Question 38

Simplify the expression: √(16x^2)

Accepted Answer

4x

Answer

2x

Answer

16x

Answer

8x

Question 39

Simplify the expression: (x - 2)^2 - (x + 2)^2

Accepted Answer

-8x

Answer

16x

Answer

32x

Answer

8x

Question 40

Which of the following is equivalent to the expression: (x^2 - 4) / (x + 2)

Accepted Answer

x - 2

Answer

2x + 4

Answer

x + 2

Answer

2x - 4

Question 41

Simplify the expression: 3x + 5x - 2x

Accepted Answer

6x

Answer

8x

Answer

10x

Answer

5x

Question 42

Apply the distributive property to simplify the expression: 2(x + 3)

Accepted Answer

2x + 6

Answer

2x + 3

Answer

x + 6

Answer

x + 3

Question 43

Factor the expression: x² - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x + 4)(x - 4)

Answer

Not factorable

Answer

(x - 2)²

Question 44

Simplify the expression: (2x² + 3x - 5) - (x² - 2x + 4)

Accepted Answer

x² + 5x - 9

Answer

x³ + x² + 1

Answer

Not simplifiable

Answer

3x² + x - 1

Question 45

Which expression is equivalent to 3(2x - 1) + 2(x + 3)?

Accepted Answer

8x + 4

Answer

5x + 7

Answer

6x - 1

Answer

9x - 5

Question 46

Factor the expression: x³ - 8

Accepted Answer

(x - 2)(x² + 2x + 4)

Answer

(x - 4)(x² + 4x + 16)

Answer

(x + 2)(x² - 2x + 4)

Answer

Not factorable

Question 47

Simplify the expression: (x + y)² - (x - y)²

Accepted Answer

4xy

Answer

x² - y²

Answer

y² - x²

Answer

x² + y²

Question 48

Which of the following is the simplified form of (x² - 1)²?

Accepted Answer

x⁴ - 2x² + 1

Answer

(x - 1)⁴

Answer

x³ - 1

Answer

x⁴ + 2x² + 1

Question 49

Simplify the expression: (3x + 2)² - (3x - 2)²

Accepted Answer

12x

Answer

24x

Answer

36x

Answer

Not simplifiable

Question 50

Factor the expression: x³ + 2x² - 5x - 6

Accepted Answer

(x + 3)(x² - 1)

Answer

Not factorable

Answer

(x + 2)(x² - 3)

Answer

(x - 3)(x² + 1)