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 (15x+ 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) + (-7y- 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 (15x+ 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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