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.
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Related Topics
- How to Multiply Monomials
- How to Multiply and Dividing Monomials
- How to Multiply Binomials
- How to Factor Trinomials
- How to Write Polynomials in Standard Form
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!
For education statistics and research National Center for Education Statistics.
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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: \(4x^3+3x^4-x^4+5x^3=2x^4+9x^3\)
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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.
- \(\color{blue}{(2x^3 – 2) + (2x^3 + 2)}\)
- \(\color{blue}{(4x^3 + 5) – (7 – 2x^3)}\)
- \(\color{blue}{(4x^2 + 2x^3) – (2x^3 + 5)}\)
- \(\color{blue}{(4x^2 – x) + (3x – 5x^2)}\)
- \(\color{blue}{(7x + 9) – (3x + 9)}\)
- \(\color{blue}{(4x^4 – 2x) – (6x – 2x^4)}\)
Download Adding and Subtracting Polynomials Worksheet
- \(\color{blue}{4x^3 }\)
- \(\color{blue}{6x^3 – 2}\)
- \(\color{blue}{4x^2 – 5}\)
- \(\color{blue}{– x^2 + 2x}\)
- \(\color{blue}{4x}\)
- \(\color{blue}{6x^4 – 8x}\)
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