Middle School Math Solutions – Polynomials Calculator, Subtracting Polynomials

In the previous post, we talked about how to add polynomials. In this post, we will talk about subtracting polynomials. The key to subtracting polynomials is to make sure that you distribute the minus sign to the expression in the parentheses. Imagine that instead of – there is a -1. This should help you visualize why you are distributing the minus sign. Once the minus sign is distributed, the minus sign will turn into a plus sign. Then, you’ll be able to add the polynomials together. Let’s see the steps for subtracting polynomials.

Steps: 

1. Distribute the negative sign
• Include this step only if there is a minus sign in front of a polynomial in parentheses
2. Remove the parentheses
• Include this step if there are polynomials in parentheses
3. Group like terms
• Put together and order like terms (terms with the same variables and the same exponent)
4. Add like terms 
• Add the coefficients of the like terms

Let’s see some examples to better understand distributing the minus sign.



First example (click here):

(x^2+2x-1)-(2x^2-3x+6)

1.  Distribute the negative sign

(x^2+2x-1)-(2x^2-3x+6)
(x^2+2x-1)-1(2x^2-3x+6)
(x^2+2x-1)+(-2x^2+3x-6)

When we imagine that there is a -1 instead of – outside the parentheses, it is easy to see and remind ourselves that we have to distribute the negative. Distributing the negative sign allows that minus sign to turn into a plus sign.

2.   Remove the parentheses

x^2+2x-1+-2x^2+3x-6
x^2+2x-1-2x^2+3x-6

3.  Group like terms

x^2+2x-1-2x^2+3x-6
x^2-2x^2+2x+3x-1-6

4.  Add like terms

x^2-2x^2+2x+3x-1-6
-x^2+5x-7

Second example (click here):

(2x^3+2x-1)-(2x^2-5x-6)

1.  Distribute the negative sign

(2x^3+2x-1)-(2x^2-5x-6)
(2x^3+2x-1)-1(2x^2-5x-6)
(2x^3+2x-1)+(-2x^2+5x+6)

2.  Remove the parentheses

2x^3+2x-1+-2x^2+5x+6
2x^3+2x-1-2x^2+5x+6

3.  Group like terms

2x^3+2x-1-2x^2+5x+6
2x^3-2x^2+2x+5x-1+6

4.  Add like terms

2x^3-2x^2+7x-1+6
2x^3-2x^2+7x+5

Last example (click here):

(4x^3-x^2+x-2)-(-x^2+3)

1.  Distribute the negative sign

(4x^3-x^2+x-2)-(-x^2+3)
(4x^3-x^2+x-2)-1(-x^2+3)
(4x^3-x^2+x-2)+(x^2-3)

2.  Remove the parentheses

4x^3-x^2+x-2+x^2-3

3.  Group like terms

4x^3-x^2+x-2+x^2-3
4x^3-x^2+x^2+x-2-3

4.  Add like terms

4x^3+x-2-3
4x^3+x-5

Subtracting polynomials takes some practice to get the hang of distributing and remembering to distribute. Once you’ve mastered adding polynomials, subtracting them should be simple. For more practice, check out Symbolab’s Practice.

Until next time,

Leah