How to Add and Subtract Polynomials? (+FREE Worksheet!)

Learn how to add and subtract polynomials and how to combine like terms and simplify polynomials in this article.

How to Add and Subtract Polynomials? (+FREE Worksheet!)

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Step by step guide to solve adding and subtracting polynomials

  • Adding polynomials is just a matter of combining like terms, with some order of operations considerations thrown in.
  • Be careful with the minus signs, and don’t confuse addition and multiplication!

Adding and Subtracting Polynomials – Example 1:

Simplify the expressions. \((2x^3-4x^4 )-(2x^4-6x^3 )=\)

Solution:

First use Distributive Property for \(-(2x^4-6x^3 )= -2x^4+6x^3 \)
\((2x^3-4x^4 )-(2x^4-6x^3 )=2x^3-4x^4-2x^4+6x^3 \)
Find “like” terms and combine them: \(2x^3+6x^3=8x^3\), \(-4x^4-2x^4=-6x^4\)

Now simplify: \(2x^3-4x^4-2x^4+6x^3=-6x^4+8x^3\)

Adding and Subtracting Polynomials – Example 2:

Add expressions. \((x^3-2)+(5x^3-3x^2 )=\)

Solution:

Remove parentheses: \((x^3-2)+(5x^3-3x^2 )=x^3-2+5x^3-3x^2\)
Combine like terms: \(x^3+5x^3=6x^3\)

Now simplify: \(x^3-2+5x^3-3x^2=6x^3-3x^2-2\)

Adding and Subtracting Polynomials – Example 3:

Subtract. \((4x^3+3x^4 )-(x^4-5x^3 )=\)

Solution:

First use Distributive Property for \(-(x^4-5x^3 )=-x^4+5x^3 \)
\( (4x^3+3x^4 )-(x^4-5x^3 )=4x^3+3x^4-x^4+5x^3 \)
Combine like terms: \(4x^3+5x^3=9x^3\), \(3x^4-x^4=2x^4\)

Now simplify: \(4x^3+3x^4-x^4+5x^3=2x^4+9x^3\)

Adding and Subtracting Polynomials – Example 4:

Add expressions. \((2x^3-6)+(9x^3-4x^2 )=\)

Solution:

Remove parentheses: \((2x^3-6)+(9x^3-4x^2 )=2x^3-6+9x^3-4x^2\)
Combine like terms: \(2x^3+9x^3=11x^3\)

Now simplify: \(2x^3-6+9x^3-4x^2=11x^3-4x^2-6\)

Exercises for Adding and Subtracting Polynomials

Simplify each expression.

  1. \(\color{blue}{(2x^3 – 2) + (2x^3 + 2)}\)
  2. \(\color{blue}{(4x^3 + 5) – (7 – 2x^3)}\)
  3. \(\color{blue}{(4x^2 + 2x^3) – (2x^3 + 5)}\)
  4. \(\color{blue}{(4x^2 – x) + (3x – 5x^2)}\)
  5. \(\color{blue}{(7x + 9) – (3x + 9)}\)
  6. \(\color{blue}{(4x^4 – 2x) – (6x – 2x^4)}\)

Download Adding and Subtracting Polynomials Worksheet

  1. \(\color{blue}{4x^3 }\)
  2. \(\color{blue}{6x^3 – 2}\)
  3. \(\color{blue}{4x^2 – 5}\)
  4. \(\color{blue}{– x^2 + 2x}\)
  5. \(\color{blue}{4x}\)
  6. \(\color{blue}{6x^4 – 8x}\)

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