Solved Examples and Worksheet for Subtracting Polynomials

Q1Subtract the polynomial 5y - 4y2 - 2 from 9y + 4 - 2y2.

A. 2y2 + 4y + 6
B. - 2y2 - 4y - 6
C. - 2y2 + 4y + 6
D. - 2y2 + 4y - 6

Solutions
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Step: 1
5y - 4y2 - 2, 9y + 4 - 2y2
  [Original polynomials.]
Step: 2
- 4y2 + 5y - 2, - 2y2 + 9y + 4
  [Write each expression in standard form.]
Step: 3
    - 2y2 + 9y + 4
(-) - 4y2 + 5y - 2
    ---------------------
       2y2 + 4y + 6
    ---------------------
  [Line up like terms vertically and subtract.]
Step: 4
The result is 2y2 + 4y + 6.
Correct Answer is :   2y2 + 4y + 6
Q2Find : (7y3 - 5y2 + 4y - 6) - (7y3 + 5y2 + 8y + 8)

A. - 10y2 - 4y - 14
B. 10y2 + 4y - 14
C. - 10y2 - 4y + 14
D. 10y2 - 4y + 14

Solutions
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Step: 1
(7y3 - 5y2 + 4y - 6) - (7y3 + 5y2 + 8y + 8)
  [Original Polynomials]
Step: 2
(7y3 - 5y2 + 4y - 6) + (- 7y3 - 5y2 - 8y - 8)
  [Add the opposite of each term in the polynomial to be subtracted.]
Step: 3
(7y3 - 7y3) + (- 5y2 - 5y2) + (4y - 8y) + (- 6 - 8)
  [Group like terms.]
Step: 4
(7 - 7)y3 + (- 5 - 5)y2 + (4 - 8)y + (- 6 - 8)
  [Use distributive property.]
Step: 5
- 10y2 - 4y - 14
  [Simplify.]
Correct Answer is :   - 10y2 - 4y - 14
Q3Find the width of the rectangular field, if the perimeter is 16y + 8 and the length is y + 4.

A. 7y
B. 6y
C. 8y
D. 9y

Solutions
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Step: 1
The perimeter of a rectangular field with length l and width w is 2(l + w).
Step: 2
16y + 8 = 2(y + 4 + w)
  [Substitue the values of the perimeter and the length in the above formula.]
Step: 3
16y + 8 = 2y + 8 + 2w
  [Distribute 2.]
Step: 4
16y + 8 - (2y + 8) = 2w
  [Subtract 2y + 8 from each side.]
Step: 5
14y = 2w
  [Simplify.]
Step: 6
7y = w
  [Divide both sides by 2.]
Step: 7
The width of the rectangular field is 7y.
Correct Answer is :   7y
Q4Find the result obtained by subtracting 2y3 - 3y2 - 4y + 3 from 4y3 - 5 + 3y2 - 6y in the vertical format.
A. 2y3 + 6y2 + 2y - 8
B. 2y3 + 6y2 - 2y - 8
C. 2y3 - 6y2 - 2y - 8
D. None of the above

Solutions
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Step: 1
2y3 - 3y2 - 4y + 3 , 4y3 - 5 + 3y2 - 6y
  [Original polynomials.]
Step: 2
2y3 - 3y2 - 4y + 3, 4y3 + 3y2 - 6y - 5
  [Write each expression in standard form.]
Step: 3
     4y3 + 3y2 - 6y - 5
(-) 2y3 - 3y2 - 4y + 3
   --------------------------
    2y3 +6 y2 - 2y - 8
   --------------------------
  [Line up like terms vertically and subtract like terms.]
Step: 4
The difference of the two polynomials is 2y3 + 6 y2 - 2y - 8.
Correct Answer is :   2y3 + 6y2 - 2y - 8
Q5Subtract the polynomial 6y - 6y2 - 4 from 10y + 6 - 4y2.
A. -2y2 + 4y + 10
B. -2y2 - 4y - 10
C. 2y2 + 4y + 10
D. -2y2 + 4y - 10

Solutions
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Step: 1
6y - 6y2 - 4, 10y + 6 - 4y2
  [Original Polynomials]
Step: 2
-6y2 + 6y - 4, -4y2 + 10y + 6
  [Write each expression in standard form.]
Step: 3
    -4y2 + 10y + 6
(-)-6y2 + 6y - 4
--------------------
      2y2 + 4y + 10
---------------------
  [Line up like terms vertically and subtract.]
Step: 4
The result is 2y2 + 4y + 10.
Correct Answer is :   2y2 + 4y + 10
Q6Subtract the polynomial 12y2 from 15y2.
A. 6y2
B. 3y2
C. 27y2
D. - 3y2

Solutions
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Step: 1
15y2 - 12y2
  [Horizontal format.]
Step: 2
= (15 - 12)y2
  [Use distributive property.]
Step: 3
= 3y2
  [As the exponents are same, subtract the coefficients.]
Correct Answer is :   3y2
Q7Subtract the polynomial 4y2 + 1 from 2y2 + 2.
A. - 2y2 - 1
B. 2y2 + 1
C. 2y2 - 1
D. - 2y2 + 1

Solutions
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Step: 1
2y2 + 2 - (4y2 + 1)
  [Write the terms.]
Step: 2
= 2y2 - 4y2 + (2 - 1)
  [Group like terms.]
Step: 3
= - 2y2 + 1
  [Simplify.]
Correct Answer is :   - 2y2 + 1
Q8Subtract the polynomial 5y - 6y2 - 4 from 9y + 6 - 4y2.
A. - 2y2 + 4y + 10
B. - 2y2 - 4y - 10
C. 2y2 + 4y + 10
D. - 2y2 + 4y - 10

Solutions
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Step: 1
5y - 6y2 - 4, 9y + 6 - 4y2
  [Original Polynomials.]
Step: 2
- 6y2 + 5y - 4, - 4y2 + 9y + 6
  [Write each expression in standard form.]
Step: 3
- 4y2 + 9y + 6
       (-) - 6y2 + 5y - 4
          .................................
             2y2 + 4y + 10
       .................................
  [Line up like terms vertically and subtract.]
Step: 4
The result is 2y2 + 4y + 10.
Correct Answer is :    2y2 + 4y + 10
Q9(7y3 - 3y2 + 2y - 7) - (7y3 + 6y2 + 7y + 5) = __________.
A. 9y2 + 5y - 12
B. - 9y2 - 5y + 12
C. 9y2 - 5y + 12
D. - 9y2 - 5y - 12

Solutions
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Step: 1
(7y3 - 3y2 + 2y - 7) - (7y3 + 6y2 + 7y + 5)
  [Original Polynomials.]
Step: 2
= (7y3 - 3y2 + 2y - 7) + (- 7y3 - 6y2 - 7y - 5)
  [Rewrite using the opposite of each term of the polynomial to be subtracted.]
Step: 3
= (7y3 - 7y3) + (- 3y2 - 6y2) + (2y - 7y) + (- 7 - 5)
  [Group like terms.]
Step: 4
= (7 - 7)y3 + (- 3 - 6)y2 + (2 - 7)y + (- 7 - 5)
  [Use distributive property.]
Step: 5
= - 9y2 - 5y - 12
  [Simplify.]
Correct Answer is :   - 9y2 - 5y - 12
Q10Find the result obtained by subtracting 3y3 - 3y2 - 4y + 4 from 5y3 - 7 + 3y2 - 6y.
A. 2y3 + 6y2 + 2y - 11
B. 2y3 + 6y2 - 2y - 11
C. 2y3 - 6y2 - 2y - 11
D. 2y3 - 6y2 + 2y - 11

Solutions
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Step: 1
3y3 - 3y2 - 4y + 4, 5y3 - 7 + 3y2 - 6y
  [Original polynomials.]
Step: 2
3y3 - 3y2 - 4y + 4, 5y3 + 3y2 - 6y - 7
  [Write each expression in standard form.]
Step: 3
5y3 + 3y2 - 6y - 7
       (-) 3y3 - 3y2 - 4y + 4
          .......................................
          2y3 + 6y2 - 2y - 11
          .......................................
  [Line up like terms vertically and subtract like terms.]
Step: 4
The result is 2y3 + 6y2 - 2y - 11.
Correct Answer is :   2y3 + 6y2 - 2y - 11
Q11What is the value of (8y2 + 5) - (- 2y3 + 13y2 - 4)?

A. y3 - 5y2 - 9
B. y3 - y2 - 9
C. 2y3 - 5y2 + 9
D. 2y3 + 5y2 + 1

Solutions
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Step: 1
(8y2 + 5) - (- 2y3 + 13y2 - 4)
Step: 2
= 8y2 + 5 + 2y3 - 13y2 + 4
  [Distributive property.]
Step: 3
= 2y3 + 8y2 - 13y2 + 5 + 4
  [Group like terms.]
Step: 4
= 2y3 - 5y2 + 9
  [Group the like terms.]
Correct Answer is :   2y3 - 5y2 + 9
Q12Find the width of the rectangular field, if the perimeter is 8y + 6 and the length is y + 3.

A. 3y
B. 4y
C. 2y
D. 5y

Solutions
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Step: 1
The perimeter of a rectangular field with length l and width w is 2(l + w).
Step: 2
8y + 6 = 2(y + 3 + w)
  [Substitue the values of the perimeter and the length in the above formula.]
Step: 3
8y + 6 = 2y + 6 + 2w
  [Distribute 2.]
Step: 4
8y + 6 - (2y + 6) = 2w
  [Subtract 2y + 6 from each side.]
Step: 5
6y = 2w
  [Simplify.]
Step: 6
3y = w
  [Divide both sides by 2.]
Step: 7
The width of the rectangular field is 3y.
Correct Answer is :   3y
Q13What is the value of (2y2 + 1) - (- 2y3 + 5y2 - 4)?
A. 2y3 - 3y2 + 5
B. 2y3 + 3y2 + 5
C. 3y3 - 2y2 + 5
D. 2y3 + 7y2 - 3

Solutions
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Step: 1
(2y2 + 1) - (- 2y3 + 5y2 - 4)
  [Original polynomial.]
Step: 2
= 2y2 + 1 + 2y3 - 5y2 + 4
  [Apply distributive property.]
Step: 3
= 2y3 + 2y2 - 5y2 + 1 + 4
  [Group like terms.]
Step: 4
= 2y3 - 3y2 + 5
  [Simplify.]
Correct Answer is :   2y3 - 3y2 + 5

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