Free Printable Simplifying Polynomials

1.

Simplify the expression.
x³(2x²+3x)

a)

2x⁵+3x⁴

b)

2x⁶+3x³

c)

5x⁹

d)

5x

2.

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

a)

5x + 10y

b)

5x + 4y

c)

5x - 4y

d)

5x -10y

3.

Simplify the expression: 2x + 1 + 7x

a)

10x

b)

10

c)

9x + 1

d)

9 + 1x

4.

n -10 +9n -3=

a)

-3

b)

9n-3

c)

n

d)

10n -13

5.

5ab – 2ab² + 4ab

a)

7ab²

b)

9ab - 2ab²

c)

ab - 2ab²

d)

12ab

6.

12x²- 8x + 9 - 7x²+ 3x - 5

a)

19x²+11x+4

b)

5x²-5x+4

c)

4x²+2x-2

d)

4

7.

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

a)

3x²- x

b)

4x²+ 2x

c)

3x² + 3x

d)

3x² + 2x

8.

(x² – 3x + 1) – (2x – 4x²)

a)

-3x² - x + 1

b)

5x² - x + 1

c)

5x²- 5x + 1

d)

-3x² - 5x + 1

9.

(3x³y)(2y⁵)

a)

3x³ + 2y⁵

b)

5x³y⁵

c)

6x³y⁶

d)

6x³y⁵

10.

(3x²)(- 2x⁴y⁵)

a)

-5x⁶y⁵

b)

-6x⁶y⁵

c)

6x⁶y⁵

d)

5x⁶y⁵

11.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

12.

-4ab(3a⁴ – b)

a)

-12a⁵b - 4ab²

b)

-12a⁵b + 4ab²

c)

-12a⁵b - b²

d)

-8a⁵b²

13.

(-3x³)(5y⁵)(-xy⁴)

a)

-15s⁶y⁹

b)

15x⁴y⁹

c)

15x⁶y⁹

d)

2x⁴y⁹

14.

3x(x² – 4x – 5)

a)

3x³- 12x² - 15x

b)

4x³- 7x² - 8x

c)

3x³- 12x - 15x

d)

4x³ - 7x² - 15x

15.

3x³y(x² – 4x – 5)

a)

3x⁵y - 12x⁴y - 15x³y

b)

4x⁵y - 12x⁴y - 15x³y

c)

4x⁵y - 27x³y

d)

3x⁵y - 12x³y - 15x³y

16.

a)

4y⁶

b)

4y²²

c)

30y⁶

d)

30y²²

17.

a)

1/m²

b)

m²

c)

m⁸

d)

1/m⁸

18.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

19.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

20.

a)

8x²y³+7x⁴+5y

b)

8x⁶y⁷-7x⁵y⁸-7x⁴y⁵

c)

8x⁶y⁷-7x⁵y⁸-5x⁴y⁵

d)

8x²y³-7xy⁴-5y

21.

Simplify the following:

$x^2-4x+3\ -2\left(3x^2+4\right)$

a)

$-5x^2-4x-5$

b)

$-5x^2-4x+3$

c)

$-9x^2-5$

d)

$5x^2-4x-5$

22.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

23.

Which expressions is not a monomial?

a)

6x³y³

b)

-7a^-1b⁷

c)

2

d)

x⁶yz⁴

24.

What is the coefficient of $-2p^2q$ ?

(a)

25.

What is the degree of $-2p^2q$ ?

(a)

26.

Simplify: 2x² + 3y - 2x + 5y + 2x

a)

2x² + 8y

b)

2x + 8y

c)

2x + 5y

d)

2x² + 4x + 8y

27.

Simplify the following monomial: $11c^2d^2-20c^2d^2$

a)

$31c^2d^2$

b)

$9c^2d^2$

c)

$-9c^2d^2$

d)

$-31c^2d^2$

28.

Simplify the following monomial: $16x^2y-4xy^2-5x^2y+10xy^2$

a)

$6xy^2+21x^2y$

b)

$11x^2y\ +6xy^2$

c)

$6x^2y+11xy^2$

29.

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

a)

5x + 5y

b)

5x + 5y + 5

c)

x + 5y + 5

d)

3x + 2y

30.

Simplify: 10m²n + 7mn² - m²n

a)

9m²n + 7mn²

b)

16m²n

c)

17m²n - mn²

d)

No change

31.

Combine like terms

$4-2r^5-7r^5+8$

a)

$-9r^5+12$

b)

$-9r^{10}+12$

c)

$-5r^5+12$

d)

$-9r^5-12$

32.

1.) Simplify
(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

33.

What is the greatest common factor of 8x²and 4x?

a)

8x²

b)

4x²

c)

2x

d)

4x

34.

What is the GCF of 2x², 6x, 4x³?

a)

6x

b)

4x

c)

2x

35.

What is the greatest common factor of 12c⁴ and 6c²?

a)

6c⁴

b)

6c²

c)

2c²

d)

12c⁴

36.

What is the GCF of 30b⁴, 45b² and 60b³?

a)

15b²

b)

5b²

c)

15b³

37.

Simplify the following monomial: $11c^2d^2-20c^2d^2$

a)

$31c^2d^2$

b)

$9c^2d^2$

c)

$-9c^2d^2$

d)

$-31c^2d^2$

38.

Simplify the following monomial: $11c^2d^2-20c^2d^2$

a)

$31c^2d^2$

b)

$9c^2d^2$

c)

$-9c^2d^2$

d)

$-31c^2d^2$

39.

Find the sum of 16y² and -5y².

a)

-11y²

b)

21y²

c)

11y²

d)

16y² - 5y²

40.

Combine like terms $7p^2-5p^3+6p^3+4p^4-9p^2$

a)

$4p^4+p^3-2p^2$

b)

$4p^4+p^6-2p^4$

c)

$4p^4+p^3+2p^2$

d)

$3p^{14}$

41.

Simplify the following monomial: $-5a^2b^{2\ }-\ a^2b^2$

a)

$-6a^2b^2$

b)

$-4a^2b^2$

c)

$6a^2b^2$

d)

$6a^2b^2$

42.

From $-9xy^2$ subtract $6xy^2$

a)

$-3xy^2$

b)

$3xy^2$

c)

$-15xy^2$

d)

$15xy^2$

43.

-3y ²+ 6y ²

a)

-3y ⁴

b)

3y ⁴

c)

-3y ²

d)

3y ²

44.

Simplify

c¹² ∗ c¹³

a)

c²⁵

b)

c¹⁵⁶

c)

c¹²³

d)

2c²⁵

45.

Simplify

(v⁵)(v⁵)

a)

v¹⁰

b)

v²⁵

c)

2v¹⁰

d)

2v²⁵

46.

Simplify

2x³ ∗ 4x⁵

a)

8x⁸

b)

6x⁸

c)

6x¹⁵

d)

8x¹⁵

47.

Simplify

x ∗ x

a)

x²

b)

2x

c)

2x²

d)

x

48.

Simplify

-4m² ∗ m²

a)

-4m⁴

b)

-3m⁴

c)

-3m²

49.

Simplify

-10k² ∗ k

a)

-10k³

b)

-10k²

c)

-9k³

d)

-9k²

50.

Simplify the expression.
x⁴ (x¹²)

a)

x³

b)

x⁴⁸

c)

x¹⁶

d)

x⁸

51.

Simplify the expression.
(6x²)(-3x⁵)

a)

18x⁷

b)

-18x⁷

c)

18x⁷

d)

3x⁷

52.

Simplify (2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

53.

In order to multiply powers with the same base, we add their exponents.

a)

True

b)

False

54.

Simplify the following expression:

3x⁴ ⋅ 6x⁶

a)

18x¹⁰

b)

9x¹⁰

c)

18x²⁴

d)

9x²⁴

55.

Simplify the following expression:

r⁶⋅ r²⋅ r³

a)

r⁶²³

b)

r¹¹

c)

11r

d)

r³⁶

56.

Simplify: 2x² + 3y - 2x + 5y + 2x

a)

2x² + 8y

b)

2x + 8y

c)

2x + 5y

d)

2x² + 4x + 8y

57.

Simplify the following monomial: $11c^2d^2-20c^2d^2$

a)

$31c^2d^2$

b)

$9c^2d^2$

c)

$-9c^2d^2$

d)

$-31c^2d^2$

58.

Simplify the following monomial: $16x^2y-4xy^2-5x^2y+10xy^2$

a)

$6xy^2+21x^2y$

b)

$11x^2y\ +6xy^2$

c)

$6x^2y+11xy^2$

59.

Find the sum of 16y² and -5y².

a)

-11y²

b)

21y²

c)

11y²

d)

16y² - 5y²

60.

4 * 4²

a)

4²

b)

16²

c)

4³

d)

16³

61.

2 * 2² *2²

a)

2⁴

b)

8⁴

c)

36

d)

2⁵

62.

Simplify:
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

63.

$\left(x^4\right)^2$

a)

$x^8$

b)

$x^6$

64.

$\left(3x^2y^2\right)^2$

a)

$9x^4y^4$

b)

$6x^4y^4$

c)

$3x^4y^4$

d)

$6x^2y^2$

65.

$-6\left(2x^5\right)^3$

a)

$-12x^8$

b)

- $-24x^{15}$

c)

$48x^{15}$

d)

$-48x^{15}$

66.

$\left(a^3\right)^2\left(b^4\right)^3$

a)

$a^5b^7$

b)

$a^6b^{12}$

67.

$\left(3xy\right)\left(-2x^2\right)^2\left(y^2\right)^5$

a)

$-6x^{3^{ }}y^{10}$

b)

$12x^5y^{11}$

c)

$-12x^5y^{11}$

d)

$-12x^5y^8$

68.

40x⁴ ÷ 8x

a)

5x³

b)

5

c)

5x⁴

d)

320x⁵

69.

3.) Simplify
(45x⁶y⁹) / (5x⁴y²)

a)

(9x²)/y⁷

b)

40x²y⁷

c)

9x²y⁷

d)

9x¹⁰y¹¹

70.

25x⁵/5x³

a)

5x

b)

5x⁸

c)

-5x²

d)

5x²

71.

Simplify.

a)

10x⁹

b)

24x¹⁴

c)

24x⁹

d)

10x¹⁴

72.

Simplify.

(2x³y)⁶

a)

2x¹⁸y⁶

b)

64x¹⁸y⁶

c)

64x³y⁶

d)

2x³y⁶

73.

Simplify.

a)

3h^1.25

b)

3h⁸⁰

c)

12h²

d)

3h²

74.

Simplify.

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

d)

none of the above

75.

Simplify.

a)

10x¹¹y⁹

b)

c)

d)

76.

When multiplying a monomial and a polynomial, the key is ....

a)

multiply the coefficients & add the exponents

b)

add the coefficients & multiply the exponents

c)

a nice, sharp pencil

77.

(5x)(2x)

a)

7x

b)

$10x^2$

c)

10x

d)

$7x^2$

78.

(4x)(-6x)

a)

-24x

b)

$-24x^2$

c)

-2x

d)

$24x^2$

79.

$\left(3x\right)\left(4x^2\right)$

a)

12x

b)

$12x^2$

c)

$12x^3$

d)

$7x^3$

80.

(5x)(x)(6x)

a)

$11x^3$

b)

30x

c)

11x

d)

$30x^3$

81.

$\left(4x^2\right)\left(x^3\right)\left(7x^2\right)$

a)

$28x^7$

b)

$28x^{12}$

c)

$12x^7$

d)

$12x^{12}$

82.

$\left(4a^2b^2\right)\left(2ab\right)$

a)

$8a^3b^3$

b)

$8a^2b^2$

c)

$6a^3b^3$

d)

$6a^2b^2$

83.

$\left(-5a^3b^2\right)\left(-2a^2b\right)$

a)

$-10a^5b^3$

b)

$10a^5b^3$

c)

$-10a^6b^2$

d)

$10a^6b^2$

84.

$\left(4x^2y\right)^3$

a)

$12x^6y^3$

b)

$12x^5y^3$

c)

$64x^6y^3$

d)

$64x^5y^3$

85.

$\left(-3xy\right)^2$

a)

$9x^2y^2$

b)

$6x^2y^2$

c)

$-9x^2y^2$

d)

$-6x^2y^2$

86.

Simplify: 2x² + 3y - 2x + 5y + 2x

a)

2x² + 8y

b)

2x + 8y

c)

2x + 5y

d)

2x² + 4x + 8y

87.

Simplify the following monomial: $11c^2d^2-20c^2d^2$

a)

$31c^2d^2$

b)

$9c^2d^2$

c)

$-9c^2d^2$

d)

$-31c^2d^2$

88.

Simplify the following monomial: $16x^2y-4xy^2-5x^2y+10xy^2$

a)

$6xy^2+21x^2y$

b)

$11x^2y\ +6xy^2$

c)

$6x^2y+11xy^2$

89.

Subtract -2x from -8x

a)

$-10x$

b)

$10x$

c)

$6x$

d)

$-6x$

90.

Simplify the expression: 2x + 1 + 7x

a)

10x

b)

10

c)

9x + 1

d)

9 + 1x

91.

Multiply (6m³n³)(8m²n³)

a)

48m⁵n⁹

b)

48m⁶n⁶

c)

48m⁵n⁶

d)

none of the above

92.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

93.

Simplify. Express using exponents. $\frac{12n^5}{4n^2}$

a)

$8n^3$

b)

$3n^3$

c)

$3n^7$

94.

Simplify. Express using exponents. $\frac{14m^3}{7m^2}$

a)

$2m^5$

b)

$2m$

c)

$7m$

95.

Simplify. Express using exponents. $\frac{9r^8}{3r^4}$

a)

$3r^{12}$

b)

$6r^4$

c)

$3r^4$

96.

Simplify. Express using exponents. $\frac{24t^9}{6t^3}$

a)

$4t^6$

b)

$18t^6$

c)

$4t^{12}$

97.

Simplify. Express using exponents. $\frac{18y^6}{2y}$

a)

$9y^7$

b)

$9y^5$

c)

$9y^6$

98.

Simplify
$\frac{10x^8y^5}{4x^2y^5}$

a)

$6x^6y$

b)

$\frac{5x^6}{2}$

c)

$\frac{5x^6y}{2}$

d)

$6x^6$

99.

Simplify.
$\frac{20x^3y^8}{30x^3y^7}$

a)

$\frac{2xy}{3}$

b)

$\frac{20y}{30}$

c)

$\frac{2y}{3}$

d)

$\frac{10y}{15}$

100.

Simplify.
$\left(x^3\right)^4\cdot\left(x^2y^3\right)^2$

a)

$x^{16}y^6$

b)

$x^{11}y^6$

c)

$x^7y^5$

d)

$x^{16}y^5$

101.

Simplify.
$\left(w^2x^5\right)^4$

a)

$w^8x^{12}$

b)

$w^8x^{20}$

c)

$w^6x^9$

d)

$w^6x^9$

102.

What is the value of 3²?

a)

6

b)

8

c)

9

d)

5

103.

What is the value of 1³³?

a)

0

b)

1

c)

33

d)

34

104.

Write 4 x 4 x 4 using an exponent.

a)

3⁴

b)

4³

c)

4 x 3

105.

Write 5 x 5 x 5 x 5 using an exponent.

a)

5³

b)

5⁴

c)

4⁵

d)

5⁵

106.

What is the value of 3⁵?

a)

15

b)

81

c)

243

d)

27

107.

What is the value of 6³?

a)

216

b)

18

c)

9

d)

42

108.

What is the value fo (-8)²?

a)

-64

b)

-16

c)

64

d)

16

109.

4⁰

a)

0

b)

1

c)

4

d)

-4

110.

How do you use exponents to represent numbers?

a)

repeated multiplication

b)

repeated addition

c)

repeated subtraction

d)

repeated division

111.

2⁵ is the same as 2 x 5.

a)

True

b)

False

112.

Name the exponent in 2³

a)

2

b)

3

c)

6

d)

8

113.

Name the base in 2³

a)

2

b)

3

c)

6

d)

8

114.

Find the value of m² – 15 when m = 8. (Remember to use substitution and evaluate the exponent first.

a)

12

b)

32

c)

49

d)

32

115.

Find the value of n² + 7 when n = 3. (Remember to use substitution and evaluate the exponent first.

a)

16

b)

17

c)

44

d)

11

116.

Find the value of 4 + b² when b = 3. (Remember to use substitution and evaluate the exponent first.

a)

10

b)

12

c)

13

d)

11

117.

Evaluate x²- 6, when x = 5.

a)

1

b)

4

c)

16

d)

19

118.

Find the Product. (2e + 3)(2e - 3)

a)

4e² - 9

b)

4e² + 9

c)

4e²- 12e - 9

d)

4e² + 12e - 9

119.

6m³n³* 8m²n³

a)

48m⁵n⁹

b)

48m⁶n⁶

c)

48m⁵n⁶

d)

none of the above

120.

$5\left(3x+7\right)$

a)

$15x+35$

b)

$8x+12$

c)

$15x+25$

d)

$14x+35$

121.

$8a^2b\ \ \ \cdot\ \ \ 3a^5\ b^2$

a)

$11a^7b^3$

b)

$24a^7b^3$

c)

$24a^7b^2$

d)

$11ab^{10}$

122.

$5\left(3x+7\right)$

a)

$15x+35$

b)

$8x+12$

c)

$15x+25$

d)

$14x+35$

123.

$8a^2b\ \ \ \cdot\ \ \ 3a^5\ b^2$

a)

$11a^7b^3$

b)

$24a^7b^3$

c)

$24a^7b^2$

d)

$11ab^{10}$

124.

$6c\ \left(3c\ +4\right)$

a)

$24c^2+18c$

b)

$18c\ +\ 24$

c)

$18c^2\ +\ 24c$

d)

$9c\ +\ 24$

125.

$2x^2\ \left(x^2-3x-10\right)$

a)

$2x^4-6x^3-20x^2$

b)

$2x^2-6x-20$

c)

$2x^4-x^3-8x^2$

d)

$3x^2-x-8$

126.

$-3m^2n\ \left(4m^2n-7mn-2\right)$

a)

$-12m^4n^2+21mn^5+6m^2n$

b)

$-12m^2n+21mn\ +\ 6$

c)

$-8mn$

d)

$-12m^4n^2+21m^3n^2+6m^2n$

127.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

128.

2x³(x²−2x − 3)

a)

2x⁶- 4x³ - 6x³

b)

2x⁵−4x⁴ − 6x³

c)

-2x⁵−4x⁴ − 6x³

d)

-2x⁶−4x³ − 6x³

129.

(2n⁴ ) (5n⁴)

a)

7n⁴

b)

10n¹⁶

c)

10n⁸

d)

none of the above

130.

Simplify: x ∙ x ∙ x ∙ x ∙ x ∙ x

a)

x⁶

b)

6x

c)

x³

d)

6x⁶

131.

6k² * k

a)

6

b)

6k

c)

6k²

d)

6k³

132.

Simplify:
x²(2x+3)

a)

x²+2x+3

b)

2x+3

c)

2x²+3x

d)

2x³+3x²

133.

Simplify the expression.
-3x²( 7x²- x + 4)

a)

-21x⁴ + 3x³ -12x²

b)

7x² - x + 4 (-3x²)

c)

21x⁴+ 3x³+ 12x²

d)

-12x²+ 3x³-21x⁴

134.

5x(4x³ + 8)

a)

9x⁴ + 40x

b)

20x⁴ + 40x

135.

4m(3m⁷ + 2m⁵)

a)

7m⁷ + 6m⁶

b)

12m⁸ + 8m⁶

136.

-8x(x - 8)

a)

-8x² + 64x

b)

-8x² - 64

137.

(3c²)(10c⁷)

a)

13c⁹

b)

30c⁵

c)

30c⁹

d)

-30c⁹

138.

6m³n³* 8m²n³

a)

48m⁵n⁹

b)

48m⁶n⁶

c)

48m⁵n⁶

d)

none of the above

139.

4m(3m⁷ + 2m⁵)

a)

7m⁷ + 6m⁶

b)

12m⁸ + 8m⁶

140.

$4ab^2\ \left(a^3b^2\ +\ 2ab\ -7a+5\right)$

a)

$4a^4b^4\ +\ 2ab\ -\ 7a\ +\ 5$

b)

$4a^4b^4\ +\ 8a^2b^3-28a^2b^2+20ab^2$

141.

4k²(6k² + 9kq - 5q²)

a)

24k² + 36k³q - 20k²q²

b)

24k⁴ + 36kq - 20k²q²

c)

24k⁴ + 36k³q - 20k²q²

d)

24k + 36 kq - 20 k²q

Simplifying Polynomials

Total questions: 141

Worksheet time: 5hrs 42mins

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