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.
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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