How to Simplify Polynomials? (+FREE Worksheet!)
To simplify polynomials, you need to find ‘like’ terms and combine them. Here you can learn how to simplify polynomials.
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Watch this practice video for additional examples and reinforcement:
Related Topics
- How to Multiply Monomials
- How to Multiply and Dividing Monomials
- How to Multiply Binomials
- How to Factor Trinomials
- How to Add and Subtract Polynomials
Step by step guide to simplifying polynomials
- Find “like” terms. (they have same variables with same power).
- Add or Subtract “like” terms using order of operation.
For education statistics and research National Center for Education Statistics.
Simplifying Polynomials – Example 1:
Simplify this expression. \(2x(2x-4)=\)
Solution:
Use Distributive Property: \(2x(2x−4)=4x^2−8x\)
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Simplifying Polynomials – Example 2:
Simplify this expression. \(4x^2+6x+2x^2-4x-3=\)
Solution:
First find “like” terms and combine them: \(4x^2+2x^2= 6x^2 \), \(6x-4x= 2x\)
Now simplify: \(4x^2+6x+2x^2-4x-3=6x^2+2x-3\)
Simplifying Polynomials – Example 3:
Simplify this expression. \(4x(6x-3)=\)
Solution:
Use Distributive Property: \(4x(6x-3)=24x^2-12x\)
Simplifying Polynomials – Example 4:
Simplify this expression. \(7x^3+2x^4+2x^3-4x^4-8x=\)
Solution:
First find “like” terms and combine them: \(7x^3+2x^3= 9x^3 \), \(2x^4-4x^4= -2x^4 \)
Now simplify and write in standard form: \(7x^3+2x^4+2x^3-4x^4-8x=-2x^4+9x^3-8x\)
Exercises for Simplifying Polynomials
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Simplify each expression.
- \(\color{blue}{(12x^3 + 28x^2 + 10x^2 + 4) }\)
- \(\color{blue}{(2x + 12x^2 – 2) – (2x + 1)}\)
- \(\color{blue}{(2x^3 – 1) + (3x^3 – 2x^3)}\)
- \(\color{blue}{(x – 5) (x – 3)}\)
- \(\color{blue}{(3x + 8) (3x – 8)}\)
- \(\color{blue}{(8x^2 – 3x) – (5x – 5 – 8x^2)}\)
Download Simplifying Polynomials Worksheet
- \(\color{blue}{12x^3 + 38x^2 + 4}\)
- \(\color{blue}{12x^2 – 3 }\)
- \(\color{blue}{3x^3 – 1}\)
- \(\color{blue}{x^2 – 8x + 15}\)
- \(\color{blue}{9x^2 – 64}\)
- \(\color{blue}{16x^2 – 8x + 5}\)
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