SUBTRACTING POLYNOMIALS WORKSHEET

Problem 1 :

Subtract 5ab from 8ab. 

Problem 2 :

Subtract (4x + 5y²)  from  (5x - y²).

Problem 3 :

Subtract (2x² + 2y² - 6)  from  (3x² - 7y² + 9).

Problem 4 :

Subtract (x³ + 4x² - x + 6) from (2x³ + 5x² - 2x + 7).

Problem 5 :

Subtract (2x³ + 7x² - 3x - 3) from (3x³ - 2x² - x + 4). 

Problem 6 :

Subtract (3 + 3x - 7x⁵ - 5x⁶) from 2(x³ - x² + 6x - 2). 

Problem 7 :

Subtract (2x³ + 5x² - 2x - 11) from (3x³ - 2x² - 5x - 6).

Problem 8 :

Subtract (x³ + 4x² - 12x - 5)  from (5x³ + 3x² + 2x - 10).

Problem 9 :

Subtract (12x³ + 14x² + 17x - 12) from (15x³ + 22x² + 17x - 19).

Problem 10 :

The profits of two different production plants can be modeled as shown below, where x' is the number of units produced at each plant. 

Eastern Plant : 

-0.03x² + 26x - 1600

Western Plant : 

-0.02x² + 20x - 1800

Write a polynomial that represents the difference of the profits at the eastern plant and the profits at the western plant.  

Detailed Answer Key

Problem 1 :

Subtract 5ab from 8ab. 

Solution : 

=  8ab - 5ab

=  3ab

Problem 2 :

Subtract (4x + 5y²)  from  (5x - y²).

Solution : 

=  (5x - y²) - (4x + 5y²)

Distributive Property. 

=  5x - y² - 4x - 5y²

Group like terms together. 

=  (5x - 4x) + (-y² - 5y²)

Combine like terms. 

=  x - 6y²

Problem 3 :

Subtract (2x² + 2y² - 6)  from  (3x² - 7y² + 9).

Solution : 

=  (3x² - 7y² + 9) - (2x² + 2y² - 6)

Distributive Property. 

=  3x² - 7y² + 9 - 2x² - 2y² + 6

Group like terms together. 

=  (3x² - 2x²) + (-7y² - 2y²) + (9 + 6)

Combine like terms. 

=  x² - 9y² + 15

Problem 4 :

Subtract (x³ + 4x² - x + 6) from (2x³ + 5x² - 2x + 7).

Solution : 

=  (2x³ + 5x² - 2x + 7) - (x³ + 4x² - x + 6)

Distributive Property. 

=  2x³ + 5x² - 2x + 7 - x³ - 4x² + x - 6

Group like terms together. 

=  (2x³ - x³) + (5x² - 4x²) + (-2x + x) + (7 - 6)

=  x³ + x² - x + 1

Problem 5 :

Subtract (2x³ + 7x² - 3x - 3) from (3x³ - 2x² - x + 4). 

Solution : 

=  (3x³ - 2x² - x + 4) - (2x³ + 7x² - 3x - 3)

Distributive Property. 

=  3x³ - 2x² - x + 4 - 2x³ - 7x² + 3x + 3

Group like terms together. 

=  (3x³ - 2x³) + (-2x² - 7x²) + (-x + 3x) + (4 + 3)

=  x³ - 9x² + 2x + 7

Problem 6 :

Subtract (3 + 3x - 7x⁵ - 5x⁶) from 2(x³ - x² + 6x - 2). 

Solution : 

=  2(x³ - x² + 6x - 2) - (3 + 3x - 7x⁵ - 5x⁶)

Distributive Property. 

=  2x³ - 2x² + 12x - 4 - 3 - 3x + 7x⁵ + 5x⁶

Group like terms together. 

=  5x⁶ + 7x⁵ + 2x³ - 2x² + (12x - 3x) + (-4 - 3)

Combine like terms. 

=  5x⁶ + 7x⁵ + 2x³ - 2x² + 9x - 7

Problem 7 :

Subtract (2x³ + 5x² - 2x - 11) from (3x³ - 2x² - 5x - 6).

Solution :

=  (3x³ - 2x² - 5x - 6 ) - (2x³ + 5x² - 2x - 11)

Distributive Property. 

=  3x³ - 2x² - 5x - 6 -2x³ - 5x² + 2x + 11

Group like terms together. 

=  (3x³ - 2x³) + (-2x² - 5x²) + (-5x + 2x) + (-6 + 11)

Combine like terms. 

=  x³ - 7x² - 3x + 5

Problem 8 :

Subtract (x³ + 4x² - 12x - 5)  from (5x³ + 3x² + 2x - 10).

Solution : 

=  (5x³ + 3x² + 2x - 10) - (x³ + 4x² - 12x - 5)

Distributive Property.

=  5x³ + 3x² + 2x - 10 - x³ - 4x² + 12x + 5

Group like terms together. 

=  (5x³ - x³) + (3x² - 4x²) + (2x + 12x) + (-10 + 5)

Combine like terms. 

=  4x³ - x² + 14x - 5

Problem 9 :

Subtract (12x³ + 14x² + 17x - 12) from (15x³ + 22x² + 17x - 19).

Solution :

=  (15x³ + 22x² + 17x - 19) - (12x³ + 14x² + 17x - 12)

Distributive Property.

=  15x³ + 22x² + 17x - 19 - 12x³ - 14x² - 17x + 12

Group like terms together. 

=  (15x³ - 12x³) + (22x² - 14x²) + (17x - 17x) + (-19 + 12)

Combine like terms. 

=  3x³ + 8x² + 0x - 7

=  3x³ + 8x² - 7

Problem 10 :

The profits of two different production plants can be modeled as shown below, where x' is the number of units produced at each plant. 

Eastern Plant : 

-0.03x² + 26x - 1600

Western Plant : 

-0.02x² + 20x - 1800

Write a polynomial that represents the difference of the profits at the eastern plant and the profits at the western plant.  

Solution :

=  Eastern plant profits - Western plant profits

=  (-0.03x² + 26x - 1600) - (-0.02x² + 20x - 1800)

Distributive Property.

=  -0.03x² + 26x - 1600 + 0.02x² - 20x + 1800

Group like terms together. 

=  (-0.03x² + 0.02x²) + (26x - 20x) + (-1600 + 1800)

Combine like terms. 

=  -0.01x² + 6x + 200

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