ADDING POLYNOMIALS WORKSHEET

Problem 1 :

Add :

(2x + 3y) and (5x + 4y)

Problem 2 :

Add :

(2a - b), (3c - 2b) and (5a - 4c)

Problem 3 :

Add :

(5x² + 2x - 7) and (6 - x - 4x²)

Problem 4 :

Add :

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

Problem 5 :

Add :

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

Problem 6 :

Add the following two polynomials. 

-1(x⁶ + x³ + 6x² - 2) and 2(5x⁶ + 7x⁵ - 3x - 3)

Problem 7 :

Add :

5(5x⁶ + 2x³ - 6x² - 2) + 6(-3x⁶ + 2x⁵ + 2x + 1)

Problem 8 :

Add :

5(x⁴ - x³ + 5) and  2(x⁴ - 5x² - 7)

Problem 9 : 

Add :

3(6x⁴ - 2x³ - 3) and 2(2x⁴ - x² - 8)

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

Use the information above to write a polynomial that represents the total profits from both plants. 

Detailed Answer Key

Problem 1 :

Add :

(2x + 3y) and (5x + 4y)

Solution : 

=  (2x + 3y) + (5x + 4y)

=  2x + 3y + 5x + 4y

Group like terms together. 

=  (2x + 5x) + (3y + 4y)

Combine like terms. 

=  7x + 7y

Problem 2 :

Add :

(2a - b), (3c - 2b) and (5a - 4c)

Solution : 

=  (2a - b) + (3c - 2b) + (5a - 4c)

=  2a - b + 3c - 2b + 5a - 4c

Group like terms together. 

=  (2a + 5a) + (-b + 2b) + (3c - 4c)

Combine like terms. 

=  7a + b - c

Problem 3 :

Add :

(5x² + 2x - 7) and (6 - x - 4x²)

Solution : 

=  (5x² + 2x - 7) + (6 - x - 4x²)

=  5x² + 2x - 7 + 6 - x - 4x²

Group like terms together. 

=  (5x² - 4x²) + (2x - x) + (-7 + 6)

Combine like terms. 

=  x² + x - 1

Problem 4 :

Add :

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

Solution : 

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

Distributive Property.

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

Group like terms together. 

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

Combine like terms. 

=  5x³ + 5x² - 4x + 1 

Problem 5 :

Add :

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

Solution : 

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

Distributive Property.

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

Group like terms together. 

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

Combine like terms. 

=  5x⁶ + 7x⁵ + 2x³ - 2x² + 9x - 7

Problem 6 :

Add the following two polynomials. 

-1(x⁶ + x³ + 6x² - 2) and 2(5x⁶ + 7x⁵ - 3x - 3)

Solution : 

=  -1(x⁶ + x³ + 6x² - 2) + 2(5x⁶ + 7x⁵ - 3x - 3)

=  -x⁶ - x³ - 6x² + 2 + 10x⁶ + 14x⁵ - 6x - 6

=  -x⁶ + 10x⁶ + 14x⁵ - x³ - 6x² - 6x + 2 - 6

=  9x⁶ + 14x⁵ - x³ - 6x² - 6x - 4

Problem 7 :

Add :

5(5x⁶ + 2x³ - 6x² - 2) + 6(-3x⁶ + 2x⁵ + 2x + 1)

Solution : 

=  5(5x⁶ + 2x³ - 6x² - 2) + 6(-3x⁶ + 2x⁵ + 2x + 1)

Distributive Property.

=  25x⁶ + 10x³ - 30x² - 10 - 18x⁶ + 12x⁵ + 12x + 6

Group like terms together. 

=  (25x⁶ - 18x⁶) + 12x⁵ + 10x³ - 30x² + 12x + (-10 + 6)

Combine like terms. 

=  7x⁶ + 12x⁵ + 10x³ - 30x² + 12x - 4

Problem 8 :

Add :

5(x⁴ - x³ + 5) and  2(x⁴ - 5x² - 7)

Solution :

=  5(x⁴ - x³ + 5) +  2(x⁴ - 5x² - 7)

Distributive Property.

=  5x⁴ - 5x³ + 25 + 2x⁴ - 10x² - 14

Group like terms together. 

=  (5x⁴ + 2x⁴) - 5x³ - 10x² + (25 - 14)

Combine like terms. 

=  7x⁴ - 5x³ - 10x² + 11

Problem 9 : 

Add :

3(6x⁴ - 2x³ - 3) and 2(2x⁴ - x² - 8)

Solution : 

=  3(6x⁴ - 2x³ - 3) + 2(2x⁴ - x² - 8)

Distributive Property.

=  18x⁴ - 6x³ - 9 + 4x⁴ - 2x² - 16

Group like terms together. 

=  (18x⁴ + 4x⁴) - 6x³ - 2x² + (-9 - 16)

Combine like terms. 

=  22x⁴ - 6x³ - 2x² - 25

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

Use the information above to write a polynomial that represents the total profits from both plants. 

Solution :

Total profits from both plants :

=  Eastern plant profits + Western plant profits

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

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

Group like terms together. 

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

Combine like terms. 

=  -0.05x² + 46x - 3400

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