Adding and subtracting polynomials worksheet answers algebra 2

Practice the questions given in the worksheet on addition of polynomials. The questions are based on arranging the expressions to find the sum of monomials, binomials, trinomials and polynomials.

1. Arrange and add the monomials:    

(i) –8abc and 10abc

(ii) 5x2yz2 and 9x2yz2

(iii) -6z7, and 5z7

2. Arrange and add the binomials:    

(i) 2p + 3q and 7p + 8q

(ii) 14x -3y and -5x + 11y

(iii) 2x2y and -8x2y

3. Arrange and add the trinomials:

(i) 4x + 5y – 3z and 9x – 6y + 4z

(ii)3x2 + 4xy + 5y2 and 9y2 – 10x2 – 6xy

(iii) 14xy + 17yz + 13xz and 8xy – 15yz + 12xz

Now we will proceed from basic to intricate problems on arranging and adding polynomials provided in the worksheet on addition of polynomials.

4. Find the sum of:

(i) 3x2 – 2xy + 4y2 and – x2 + 4xy – 2y2

(ii) 3p + 4q + 7r, -5p + 3q – 6r and 4p – 2q – 4r

(iii) 2a2 + ab - b2, -a2 + 2ab + 3b2 and 3a2 – 10ab + 4b2

(iv) k2 – k + 1, -5k2 + 2k – 2 and 3k2 – 3k + 1

(v) x2 – xy + yz, 2xy + yz – 2x2 and -3yz + 3x2 + xy

(vi) 4u2 + 7 – 3u, 4u – u2 + 8 and -10 + 5u – 2u2

5. Add the following expressions:

(i) 3xyz + 4yz + 5zx, 7xz – 6yz + 4xyz and -9xyz – 11zy + 9xz

(ii) x3 – 2y3 + x, y3 – 2x3 + y and -2y + 2y3 – 5x + 4x3

(iii) 7p2 – 4p2q + 8q2, 5q2 – 2p2 + 6p2q and 3p2q + 10p2

(iv) 9x2 – 7x + 5, -14x2 – 6 + 15x and 20x2 + 40x - 17

(v) –m2 – 3mn + 3n2 + 8, 3m2 – 5n2 – 3 + 4mn and -6mn + 2m2 – 2 + n2

6. If P = a2 – 2bc + b2, Q = -b2 + bc – c2 and R = c2 + cb + a2 then, find the value of P + Q + R.

Answers for the worksheet on addition of polynomials are given below to check the exact answers of the above addition.

Answers:

1. (i) 2abc

(ii) 14x2yz2

(iii) -z7

2. (i) 9p + 11q

(ii) 9x + 8y

(iii) -6x2y

3. (i) 13x - y +z

(ii) -7x2 - 2xy + 14y2

(iii) 22xy + 2yz + 25xz

4. (i) 2x2 + 2xy + 2y2

(ii) 2p + 5q – 3r

(iii) 4a2 – 7ab + 6b2

(iv) –k2 – 2k

(v) 2x2 + 2xy - yz

(vi) u2 + 6u + 5

5. (i) -2xyz – 13yz + 21xz

(ii) 3x3 + y3 – 4x – y

(iii) 15p2 + 5p2q + 13q2

(iv) 15x2 – 32x – 18

(v) 4m2 – 5mn – n2

6. 0

● Terms of an Algebraic Expression - Worksheet

Worksheet on Types of Algebraic Expressions

Worksheet on Degree of a Polynomial

Worksheet on Addition of Polynomials

Worksheet on Subtraction of Polynomials

Worksheet on Addition and Subtraction of Polynomials

Worksheet on Adding and Subtracting Polynomials

Worksheet on Multiplying Monomials

Worksheet on Multiplying Monomial and Binomial

Worksheet on Multiplying Monomial and Polynomial

Worksheet on Multiplying Binomials

Worksheet on Dividing Monomials

6th Grade Math Practice

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

While addition and subtraction of polynomials, we simply add or subtract the terms of the same power. The power of variables in a polynomial is always a whole number, power can not be negative, irrational, or a fraction. It is straightforward to add or subtract two polynomials. A polynomial is a mathematics expression written in the form of \(a_0x^n + a_1x^{n-1} + a_2x^{n-2} + ...... + a_nx^{0}\).

The above expression is also called polynomial in standard form, where \(a_0, a_1, a_2.........a_n\) are constants, and n is a whole number. For example x2 + 2x + 3,   5x4 - 4x2 + 3x +1 and 7x - √3 are polynomials.

How Can We Add Polynomials?

The addition of polynomials is simple. While adding polynomials, we simply add like terms. We can use columns to match the correct terms together in a complicated sum. Keep two rules in mind while performing the addition of polynomials.

• Rule 1:  Always take like terms together while performing addition.
• Rule 2:  Signs of all the polynomials remain the same.

For example, Add 2x2 + 3x +2 and 3x2 - 5x -1

• Step 1: Arranging the polynomial in standard form. In this case, they are already in their standard forms.
• Step 2:  Like terms in the above two polynomials are:
  2x2 and 3x2; 3x and -5x; 2 and -1.
• Step 3: Calculations with signs remaining same:

Like Terms

Like Terms are terms whose variables, along with their exponents, are the same. For example, 2x, 7x, -2x, etc are all like variables.

Unlike Terms

Unlike Terms are terms whose either variables, exponents, or both variables and exponents are the not same. For example, 2, 7x2, -2y2, etc are all unlike variables.

Subtraction of Polynomials

The subtraction of polynomials is as simple as the addition of polynomials. Using columns would help us to match the correct terms together in a complicated subtraction. While subtracting polynomials, separate the like terms and simply subtract them. Keep two rules in mind while performing the subtraction of polynomials.

• Rule 1: Always take like terms together while performing subtraction.
• Rule 2: Signs of all the terms of the subtracting polynomial will change, + changes to - and - changes to +.

For example, we have to subtract 2x2 + 3x +2 from 3x2- 5x -1

• Step 1: Arranging the polynomial in standard form. In this case, they are already in their standard forms.
• Step 2:  Like terms in the above two polynomials are: 2x2 and 3x2;3x and -5x;2 and  -1
• Step 3: Enclose the part of the polynomial which to be deducted in parentheses with a negative (-) sign prefixed. Then, remove the parentheses by changing the sign of each term of the polynomial expression.
• Step 4: Calculations after altering the signs of the subtracting polynomials:

Steps for Adding and Subtracting Polynomials

The addition or subtraction of polynomials is very simple to perform, all we need to do is to keep some steps in mind. To perform the addition and subtraction operation on the polynomials, the polynomials can be arranged vertically for complex expressions. For simpler calculations, we can perform the operation using the horizontal arrangement.

Adding and Subtracting Polynomials Horizontally

Polynomials can be added and subtracted in horizontal arrangement using the steps given below,

• Step 1: Arrange the polynomials in their standard form.
• Step 2: Place the polynomial next to each other horizontally. 
• Step 3: First separate the like terms. 
• Step 4: Arrange the like terms together.
• Step 5: Signs of all the polynomials remain the same in addition. While in Subtraction, the signs of the terms in subtracting polynomial change.
• Step 6: Perform the calculations.

Adding and Subtracting Polynomials Vertically

Polynomials can be added and subtracted in vertical arrangement using the steps given below,

• Step 1: Arrange the polynomials in their standard form
• Step 2: Place the polynomials in a vertical arrangement, with the like terms placed one above the other in both the polynomials.
• Step 3: We can represent the missing power term in the standard form with "0" as the coefficient to avoid confusion while arranging terms.
• Step 4: Signs of all the polynomials remain the same in addition. While in Subtraction, the signs of the terms in subtracting polynomial change.
• Step 5: Perform the calculations

By following these steps we can solve adding and subtracting polynomials.

Example: (3x3 + x2 - 2x -1) + (x3 + 6x + 3).

The given polynomials are arranged in their standard forms.

Addition performed horizontally:

• Step 1: Separate the like terms: 3x3 and x3; x2; -2x and 6x; -1 and 3
• Step 2: Arrange the like terms together: 3x3 + x3 + x2 + (-2x + 6x) + (-1 + 3)
• Step 3: Perform the calculations: (3 + 1)x3 + x2 + (-2 + 6)x + (-1 + 3)= 4x3 + x2 + 4x + 2

Addition performed vertically:

• Step 1: Arrange both the polynomials one above the other with like terms place one above the other. We can represent the missing power term in the standard form with "0" as the coefficient to avoid confusion while arranging terms.
• Step 2: Perform the calculations.

\[ \begin{align} \ \ 3x^3 + x^2 - 2x -1 \\ + \ x^3 + 0x^2 + 6x + 3 \\ \hline \\ 4x^3 + x^2 + 4x + 2 \\ \hline \end{align}\]

Important Notes:

• The highest power of the variable in a polynomial is called the degree of the polynomial. 
• The algebraic expressions having negative or irrational power of the variable are not polynomials.
• Addition and subtraction in polynomials can only be performable on like terms. 

Challenging Question on Adding and Subtracting Polynomials

Find the value of a if the addition of the polynomials (a-2)x3 + 3x2 + 4x -1 and (2a + 1)x3 + 2x2 - 6x - 3 is a quadratic polynomial.

FAQs on Adding and Subtracting Polynomials

How do We Add or Subtract Polynomials?

Adding or subtracting polynomials is simple. While adding or subtracting polynomials we need to keep the rules for adding and subtracting a polynomial in mind. The rules can be explained as,

• Rule 1:  Always take like terms together while performing addition or subtraction.
• Rule 2: Signs of all the polynomials remain the same in addition. While in Subtraction, the signs of the subtracting polynomials change.

What are Binomials?

Binomials are polynomials that contain only two terms. For example x2 + y2 and 3x + 2y are binomials. For example, x + y +  z is not a binomial.

What is the Main Thing to Remember When you are Adding and Subtracting Polynomials?

The main thing to remember while performing addition and subtraction on polynomials is:

• to keep in mind the concept of like terms
• when a polynomial multiplied with a negative sign, all the signs will be changed. i.e., + to - and - to +

How do you Combine Like Terms?

While combining like terms, such as 2x and 7x, we simply add their coefficients. For example, 2x + 7x = (2+7)x = 9x.

What are Like Terms?

Like Terms are terms whose variables, along with their exponents, are the same. For example, 2x, 7x, -2x, etc are all like variables.

Can you Combine Terms with Different Exponents?

No, you can only combine terms with the exact same variable and the exact same exponent. That means you can only combine squared variable terms with squared variable terms, cubed variable terms with cubed variable terms, etc.