SUBTRACTING POLYNOMIALS
Consider the two polynomials A and B.
You want to find (A - B).
That is, you want to subtract polynomial B from polynomial A.
The following steps will be useful to do the above subtraction of polynomials.
Step 1 :
To subtract the polynomial B from polynomial A, write the polynomials in the form :
A - B
Step 2 :
Use Distribute Property.
That is, distribute negative sign to all the terms of polynomial B.
Step 3 :
Group like terms together.
Step 3 :
Combine like terms.
Example 1 :
Subtract 5ab from 8ab.
Solution :
= 8ab - 5ab
= 3ab
Example 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
Example 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
Example 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
Example 5 :
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
Example 6 :
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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