Master Algebraic Expressions: Simplify, Expand, and Factorize with Confidence

Question 1

Simplify the expression: 2x + 5 - 3x

Accepted Answer

x - 5

Answer

x + 5

Answer

-x + 5

Answer

-x - 5

Question 2

Expand and simplify the expression: 3(2x - 5)

Accepted Answer

6x - 15

Answer

6x + 15

Answer

5x - 15

Answer

5x + 15

Question 3

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

Accepted Answer

2x + 6

Answer

-x + 6

Answer

-2x + 6

Answer

x + 2

Question 4

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

Accepted Answer

x^6y^3

Answer

x^5y^3

Answer

x^2y^9

Answer

x^9y^3

Question 5

Which of the following is a quadratic expression?

Accepted Answer

x^2 - 3

Answer

-x + 2

Answer

2x - 5

Answer

√x + 1

Question 6

Solve for x: x^2 - 9 = 0

Accepted Answer

x = ±3

Answer

x = 3

Answer

x = 9

Answer

x = ±9

Question 7

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

Accepted Answer

6x

Answer

2x

Answer

10x

Answer

x

Question 8

Expand the expression: (2x + 3)(x - 1)

Accepted Answer

2x^2 - x + 3x - 3

Answer

2x^2 + 2x - 3x - 3

Answer

x^2 - x + 3x - 3

Answer

2x^2 + x - 3x - 3

Question 9

Simplify the expression: (x + 2)^2

Accepted Answer

x^2 + 4x + 4

Answer

x^2 + 2x + 4

Answer

x^2 - 4x + 4

Answer

x^2 + 4

Question 10

Simplify the expression: (x - y)/(x + y) * (x + y)/(x - y)

Accepted Answer

1

Answer

-1

Answer

y/x

Answer

x/y

Question 11

Expand the expression: (a + b)^3

Accepted Answer

a^3 + b^3 + 3a^2b + 3ab^2

Answer

a^3 + b^3 - 3a^2b + 3ab^2

Answer

a^3 - b^3 + 3a^2b - 3ab^2

Answer

a^3 - b^3 - 3a^2b + 3ab^2

Question 12

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

Accepted Answer

x^2 - 5x + 6

Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 + 5x + 6

Question 13

Solve for x: 3x + 5 = 14

Accepted Answer

x = 4

Answer

x = 3

Answer

x = 5

Answer

x = 6

Question 14

Simplify the expression: (x + 2)^2

Accepted Answer

x^2 + 4x + 4

Answer

x^2 + 4

Answer

x^2 + 2x + 4

Answer

x^2 - 4x + 4

Question 15

Factorize the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Answer

Cannot be factorized.

Question 16

Which expression is equivalent to **4x(2x-1) + 3(2x-1)?**

Accepted Answer

(8x² - 4x) + (6x - 3)

Answer

(8x² - 4x) + (3x - 3)

Answer

(4x² - 2x) + (3x - 3)

Answer

(4x² - 2x) + (6x - 3)

Question 17

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

Accepted Answer

5x - 5

Answer

x - 5

Answer

x + 5

Answer

5x + 5

Question 18

Expand the following expression: **(x + 2)(x - 3)**

Accepted Answer

x² - 5x + 6

Answer

x² + x - 6

Answer

x² - x - 6

Answer

x² + 5x + 6

Question 19

Factorise the following expression: **x² - 9**

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Question 20

Which of the following is equivalent to **2x(x + 3)?**

Accepted Answer

2x² + 6x

Answer

2x + 3

Answer

2x² - 6x

Answer

x² + 6x

Question 21

Simplify the expression x^2 + 6x + 8 by factorising it.

Accepted Answer

(x + 2)(x + 4)

Answer

(x - 2)(x - 4)

Answer

(x + 8)(x - 1)

Answer

Cannot be factorised

Question 22

Solve the inequality 2x + 5 > 11. What is the value of x that satisfies this inequality?

Accepted Answer

x > 3

Answer

x < 3

Answer

x < -3

Answer

x > -3

Question 23

Factorise the expression x^2 - 4 using the difference of squares formula.

Accepted Answer

(x - 2)(x + 2)

Answer

(x + 2)(x + 2)

Answer

(x - 2)(x - 2)

Answer

(x + 2)(x - 2)

Question 24

Solve the equation x + 5 = 12. What is the value of x?

Accepted Answer

7

Answer

8

Answer

9

Answer

10

Question 25

Which of the following expressions represents the area of a rectangle with length x and width y?

Accepted Answer

xy

Answer

x + y

Answer

x - y

Answer

2(x + y)

Question 26

Factorize the expression: x² + 6x + 8

Accepted Answer

(x + 2)(x + 4)

Answer

(x - 2)(x - 4)

Answer

(x + 8)(x + 1)

Answer

(x - 8)(x - 1)

Question 27

Expand the expression: (x - 3)², what is the result?

Accepted Answer

x² - 3x + 9

Answer

x² + 3x + 9

Answer

x² - 6x + 9

Answer

x² + 6x + 9

Question 28

Which of the following is an algebraic expression?

Accepted Answer

5x + 2

Answer

x = 5

Answer

y > 10

Answer

2^3

Question 29

Which of the following is equivalent to the expression: 2x(x - 3)?

Accepted Answer

2x² - 3x

Answer

2x² + 3x

Answer

x² - 6x

Answer

x² + 6x

Question 30

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

Accepted Answer

5x + 2

Answer

5x - 2

Answer

x + 8

Answer

2x + 5

Question 31

Which of the following is an example of a polynomial expression?

Accepted Answer

x^3 - 2x^2 + 5x - 1

Answer

2x + 3

Answer

1/(x - 2)

Answer

sqrt(x) + 1

Question 32

Simplify the expression: (a + b)^2 - (a - b)^2

Accepted Answer

4ab

Answer

0

Answer

2ab

Answer

8ab

Question 33

Factor the expression x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)^2

Answer

Cannot be factored

Answer

(x + 3)^2

Question 34

Factor the expression 4x^2 - 25

Accepted Answer

(2x + 5)(2x - 5)

Answer

Cannot be factored

Answer

(2x - 5)^2

Answer

(2x + 5)^2

Question 35

What do you get when you expand the expression 2(x + 3)?

Accepted Answer

2x + 6

Answer

x + 6

Answer

2x + 3

Question 36

Factorize the expression 4x + 8 by finding the greatest common factor.

Accepted Answer

4(x + 2)

Answer

x(4 + 8)

Answer

4(x + 8)

Answer

2(2x + 4)

Question 37

Which expression is the same as 5(x - 2)?

Accepted Answer

5x - 10

Answer

5x - 2

Answer

x - 10

Answer

5x + 10

Question 38

Simplify the expression 2(x + y) - (x - y) by combining like terms.

Accepted Answer

x + 3y

Answer

x - 3y

Answer

3x + 3y

Answer

3x + y

Question 39

Factorize the expression x² - 9 using the difference of squares pattern.

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 3)²

Answer

(x + 9)(x - 9)

Answer

(x - 3)²

Question 40

What is the number in front of the 'x' term in the expression 4x² - 7x + 5?

Accepted Answer

-7

Answer

7

Answer

4

Answer

-4

Question 41

Which expression represents the total length of the sides of a rectangle with length 'l' and width 'w'?

Accepted Answer

2l + 2w

Answer

l² + w²

Answer

l × w

Answer

l + w

Question 42

If x = 4, what is the value of the expression 3x + 5?

Accepted Answer

17

Answer

27

Answer

12

Answer

22

Question 43

Simplify the expression 4a + 7b - 2a + 3b by combining like terms.

Accepted Answer

2a + 10b

Answer

6a + 10b

Answer

2a - 4b

Answer

6a - 4b

Question 44

What is the expanded form of the expression 3(2x - 5)?

Accepted Answer

6x - 15

Answer

6x - 5

Answer

5x - 8

Answer

5x - 15

Question 45

Simplify the expression: 5p - 2(p + 3)

Accepted Answer

3p - 6

Answer

7p - 6

Answer

7p + 6

Answer

3p + 6

Question 46

A square has a perimeter of 4x. What is the length of one side?

Accepted Answer

x

Answer

4

Answer

2x

Answer

16x

Question 47

What is the number in front of the 'y' in the expression 8x - 2y + 5?

Accepted Answer

-2

Answer

8

Answer

5

Answer

2

Question 48

A rectangle has a length of (2x + 3) cm and a width of (x - 1) cm. What is the area of the rectangle?

Accepted Answer

(2x² + x - 3) cm²

Answer

(2x² - 3) cm²

Answer

(3x + 2) cm²

Answer

(3x - 2) cm²

Question 49

The rule for a number pattern is 'multiply the position number by 3 and then subtract 1'. What is the 5th number in the pattern?

Accepted Answer

14

Answer

17

Answer

2

Answer

11

Question 50

Which of these is the same as x² - 9?

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 9)(x - 1)

Answer

(x + 3)²

Answer

(x - 3)²