Subtraction of Polynomials

Subtraction of polynomials can be solved in two methods.

Follow the following steps to solve in the first method:

(i) Enclose the part of the expression to be subtracted in parentheses with a negative (-) sign prefixed

(ii) Remove the parentheses by changing the sign of each term of the polynomial expression which is in the parentheses.

(iii) Arrange the like terms.

(iv) Finally add the like terms to find the required subtraction.

For example:

1. Subtract: 2x - 5y + 3z from 5x + 9y - 2z.

First we need to enclose the first part which is to be subtracted in parentheses with a negative (-) sign prefixed.

5x + 9y - 2z – (2x - 5y + 3z)

Now we need to remove the parentheses by changing the sign of each term which is in the parentheses.

= 5x + 9y - 2z – 2x + 5y - 3z

= 5x – 2x + 9y + 5y - 2z - 3z, by arranging the like terms.

= 3x + 14y - 5z


2. Subtract: -6x2 - 8y3 + 15z from x2 – y3 + z.

First we need to enclose the first part which is to be subtracted in parentheses with a negative (-) sign prefixed.

x2 - y3 + z – (-6x2 - 8y3 + 15z)

Now we need to remove the parentheses by changing the sign of each term which is in the parentheses.

= x2 - y3 + z + 6x2 + 8y3 - 15z

= x2 + 6x2 - y3 + 8y3 + z - 15z, by arranging the like terms.

= 7x2 + 7y3 - 14z

Follow the following steps to solve the subtraction of polynomials in the second method:

Re-write the given expressions in two lines such that the lower line is the expression to be subtracted and like terms of both the expressions are one below the other.

Change the sign of each term in the lower line i.e. change the sign of each term of the expression to be subtracted.

Combine the terms column-wise with new signs assigned to the terms of lower line.  

For example:

1. Subtract: x – 4y – 2z from 7x – 3y + 6z

First we will arrange the expressions in two lines such that the lower line of the expression is to be subtracted from the other, placing the like terms in the same column one below the other.

Subtraction of Polynomials

Now by changing the sign (positive becomes negative and negative becomes positive) of each term in the lower line i.e. change the sign of each term of the expression to be subtracted (x – 4y – 2z).

Therefore, the required answer is 6x +   y + 8z.


2. Subtract: 3a3 + 5a2 – 7a + 10 from 6a3 - 8a2 + a + 10

First we will arrange the expressions in two lines such that the lower line of the expression is to be subtracted from the other, placing the like terms in the same column one below the other.

Polynomials Subtraction

Now by changing the sign (positive becomes negative and negative becomes positive) of each term in the lower line i.e. change the sign of each term of the expression to be subtracted (3a3 + 5a2 – 7a + 10).
Therefore, the required answer is 3a3 - 13a2 + 8a.

Thus, we have learnt how to solve subtraction of polynomials in both the methods.

Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials







6th Grade Math Practice

From Subtraction of Polynomials to HOME PAGE




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.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Divisible by 10 | Test of Divisibility by 10 Video | Rules | Examples

    Mar 29, 25 03:06 PM

    Divisible by 10
    Divisible by 10 is discussed below. A number is divisible by 10 if it has zero (0) in its units place. Consider the following numbers which are divisible by 10, using the test of divisibility by 10:

    Read More

  2. Divisible by 9 | Test of Divisibility by 9 | Rules | Video | Examples

    Mar 29, 25 02:55 PM

    Divisible by 9
    A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9. Consider the following numbers which are divisible by 9, using the test of divisibility by 9:

    Read More

  3. Divisible by 6 | Rules for Test of Divisibility by 6 Video | Examples

    Mar 29, 25 02:48 PM

    Divisible by 6
    Divisible by 6 is discussed below: A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42

    Read More

  4. Divisible by 5 | Rules for Test of divisibility by 5 | Video |Examples

    Mar 29, 25 02:43 PM

    Divisible by 5
    Divisible by 5 is discussed below: A number is divisible by 5 if its units place is 0 or 5. Consider the following numbers which are divisible by 5, using the test of divisibility by

    Read More

  5. Divisibility Rules From 2 to 18 | Math Divisibility Test | Videos |

    Mar 29, 25 02:17 PM

    Divisibility Rules
    To find out factors of larger numbers quickly, we perform divisibility test. There are certain rules to check divisibility of numbers. Divisibility tests of a given number by any of the number 2, 3, 4…

    Read More

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