Free Printable Algebraic Expressions Review 2025

1.

Classify by number of terms:
3x³ – 6x

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

2.

How many terms are in this polynomial?

2x³- 8x²+ 3x - 7

a)

7

b)

1

c)

4

d)

2

3.

What is the constant of this polynomial?

2x³- 8x²+ 3x - 7

a)

2

b)

-8

c)

3

d)

-7

4.

What is the coefficient of this term?

9x³

a)

None

b)

9

c)

3

d)

x

5.

Classify by number of terms:

5x² – 6x + 3

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

6.

Simplify the Expression:

3x + 6 - 2x +7

a)

14

b)

14x

c)

x + 13

d)

x - 13

7.

Classify:
2n³

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

8.

What are like terms?
Terms that have....

a)

the same variables

b)

the same exponents

c)

the same coefficients

d)

the same variables and exponents

9.

The number in front of the variable is called the....

a)

exponent

b)

base

c)

coefficient

d)

fronter

10.

Which pair is an example of like terms?

a)

2a and 2b

b)

x and x²

c)

3k and 3k³

d)

y² and 2y²

11.

Simplify this polynomial:

n - 10 + 9n - 3

a)

-3

b)

9n - 3

c)

n

d)

10n - 13

12.

Combine like terms
3x + 2x + 3y - 7y

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

13.

Simplify by combining like terms:
4x² - 3x + 11 -2x

a)

4x² - 5x + 11

b)

11x + 11

c)

16x² - 5x + 11

d)

10x²

14.

Simplify this polynomial:

3x²- x + 2 - 5x²+ 8x - 5

a)

8x²+ 9x + 7

b)

-2x²+ 7x - 3

c)

2x²+ 7x - 3

d)

5x²- 3

15.

Classify the polynomial and give the degree:

5x³y²

a)

Monomial, 3

b)

Uninomial, 3

c)

Uninomial, 5

d)

Monomial, 5

16.

Find the sum.

(3 - 2x + 2x²) + (4x - 5 + 3x²)

a)

7x - 7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x + 8

17.

What is the perimter of square with side length 2X?

a)

4x

b)

10x

c)

8x

d)

6x

18.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

19.

$\left(8x+8y-8\right)\div8$

a)

$1$

b)

$x+y-1$

c)

$x+y$

d)

$2xy-1$

20.

The perimeter of a square can be shown by the expression: $40x^5-32x^3+4x-8$
What is the length of each side of the square?

a)

$10x^4-8x^2+x+2$

b)

$10x^5-8x^3+x-2$

c)

$36x^5-28x^3-4$

d)

$10x^5+8x^3-x+2$

21.

Combine like terms:

-m + 17m - 12c + 3m + 4c + 21c

a)

19m + 13c

b)

21m + 37c

c)

20m + 12c

d)

19m - 12c

22.

What is the perimeter of a rectangle, in terms of x, with length of 4x - 9 and a length of 8x + 2?

a)

$32x^2-64x-18$

b)

12x - 7

c)

$32x^2-18$

d)

24x -14

23.

$Simplify:\ \ 5x^2\ +\ 14y\ -9y\ +\ x^2\ -7x^2-y$

a)

$13x^2+\ 24y$

b)

$-13x^2\ +\ 13y$

c)

$-x^2\ +\ 4y$

d)

$x^2\ -\ 4y$

24.

What is the perimeter of a square in terms of m, with a side of $7m\ -\ 3$ ?

a)

$14m\ -\ 6$

b)

$28m\ -\ 12$

c)

$49m^2-\ 42m\ +\ 9$

d)

$49m^2\ +\ 9$

25.

$Simplify:\ \ -6h^2\ +2j\ -\ 14h^2-\ h^2\ +\ 15j$

a)

$-20h^2+\ 13j$

b)

$20h^2\ +\ 17j$

c)

$-21h^2\ +\ 17j$

d)

$-21h^4\ +\ 17j$

26.

The three lengths of an isosceles triangle are 23g - 5, 16g + 7 and 14g + 12. What is the perimeter of the triangle in terms of g?

a)

52g + 13

b)

54g + 17

c)

55g - 12

d)

53g + 14

27.

Simplify: 29u + 4d - 13u + 2u + 7d

a)

18u + 11d

b)

44u + 11d

c)

18u - 3d

d)

31u + 28d

28.

-3(x - 4)

a)

-3x - 12

b)

3x - 12

c)

3x + 12

d)

-3x + 12

29.

(2x + 5y - z) + (-6x - 4y + 7z)

a)

-4x² +6y² + 6z²

b)

4x + y + 6z

c)

-4x² - y² + 6z²

d)

-4x + y + 6z

e)

None of these

30.

(3x + 4y - 3z) - (2x - 6y + 7z)

a)

x + 10y - 10z

b)

-x +10y - 10z

c)

x -10y - 10z

d)

-x -10y - 10z

31.

Subtract: (2a² + 5a + 3) - (a² - 3a - 4)

a)

3a² + 2a - 1

b)

a²+ 8a + 7

c)

3a²+ 8a + 7

d)

a² + 2a - 1

32.

Add: (3x² + 2x + 1) + (2x² - 4x - 5) + (3x - 1)

a)

5x² + 6x - 7

b)

8x²- 3x - 5

c)

5x²+ x - 5

d)

6x² + 8x + 5

33.

What is (3x² + 2x - 6) - (2x² - 3x + 1)

a)

1x² + 5x + 5

b)

1x² - 5x - 7

c)

1x² + 5x - 7

d)

1x² - 5x + 7

34.

(2x² + 5xy + 4y²) - (-xy - 6x² + 2y²)

a)

-4x² + 4xy + 6y²

b)

8x² + 6xy + 2y²

c)

8x² + 4xy - 2y²

d)

4x² + 6xy + 6y²

35.

Subtract

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

a)

-8n² - 8n + 3

b)

-7n² - 8n + 3

c)

-6n²- 8n + 3

d)

-7n² - 4n + 3

36.

Simplify the following expression:
-8 (5b + 2) -7 (b - 5)

a)

-33b + 19

b)

-47b² + 21

c)

33b - 19

d)

-47b +19

37.

a)

5w² − 4w + 3

b)

12w² − 9w + 6

c)

12w² − 12w + 9

d)

5w² − 12w+ 9

38.

Expand and simplify the following expression:

$2\ \left(x-3\right)-4\left(x-5\right)$

a)

$2x-26$

b)

$-6x-26$

c)

$2x^2-10x-20$

d)

$-2x+14$

39.

Divide $\frac{-20p^2-16p+8}{-4}$

a)

-5p²- 4p + 2

b)

$5p^{2\ }+4p-2$

c)

5p + 4

d)

$5p^{2\ }+4p+2$

40.

Find the perimeter of the shape

a)

11a + 6

b)

11a - 1

c)

11a - 13

d)

11a + 7

41.

Find the perimeter of the shape

a)

17a - 2b - 3

b)

13a + 17b - 3

c)

15a + 3b - 5

d)

18a - 6b + 9

42.

What is the Perimeter?

a)

3x - 3 inches

b)

6x - 6 inches

c)

3x - 6 inches

d)

6x - 3 inches

43.

The perimeter of the
triangle is $10x+20$ . Find the length of the missing side.

a)

$6x+10$

b)

$15x+30$

c)

$5x+10$

d)

$5x-10$

44.

Find the area of a rectangle with length (x - 5) and width (3x + 1).

a)

3x²+16x-5

b)

3x²-14x+5

c)

3x²-14x-5

45.

Find the perimeter of a square with side length of

x+2

a)

$4x+8$

b)

$2x+4$

c)

$x^2+4x+4$

d)

$4x^4+8$

46.

What is the perimeter of the rectangle?

a)

x²+8x-5

b)

2x²+16x-10

c)

2x²+10x-8

d)

6x-2

47.

Find the perimeter of the triangle

a)

$4x+64$

b)

$4x^2+64$

c)

$3x+50$

d)

$3x^2+50$

48.

Simplify
$-4\left(2d+3b\right)$
When b = -9 and d = -6

a)

0

b)

144

c)

-144

d)

156

49.

Simplify
$9c+5z+2$
When c = -9 and z = 9

a)

128

b)

-124

c)

-34

50.

Simplify
$-8\left(-3x-4z\right)$
When x = -6 and z = 3

a)

240

b)

-48

c)

48

d)

-240

51.

What is the degree of the monomial?

2x²y³z

a)

6

b)

3

c)

5

d)

2

52.

What is the degree of the monomial?

−xy⁴

a)

1

b)

-1

c)

4

d)

5

53.

What is the degree of the monomial?

a)

5

b)

3

c)

8

d)

9

54.

Multiply

a)

b)

c)

d)

55.

Find the product: $\left(3\right)\left(4a^2\right)\left(2b\right)$

a)

$24a^2b^{ }$

b)

$24a^3b^3$

56.

Write a polynomial expression for the area of the triangle. HINT: A= $\frac{b\times h}{2}$

a)

18x² - 54x

b)

9x² + 9

c)

36x² + 108x

d)

9x² + 27x

Algebraic Expressions Review 2025

Total questions: 56

Worksheet time: 3hrs 48mins

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