How to Simplify Polynomials? (+FREE Worksheet!)

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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 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.

Simplifying Polynomials 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

Simplifying Polynomials

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Simplify each expression.

1. \(\color{blue}{(12x^3 + 28x^2 + 10x^2 + 4) }\)
2. \(\color{blue}{(2x + 12x^2 – 2) – (2x + 1)}\)
3. \(\color{blue}{(2x^3 – 1) + (3x^3 – 2x^3)}\)
4. \(\color{blue}{(x – 5) (x – 3)}\)
5. \(\color{blue}{(3x + 8) (3x – 8)}\)
6. \(\color{blue}{(8x^2 – 3x) – (5x – 5 – 8x^2)}\)

Download Simplifying Polynomials Worksheet

1. \(\color{blue}{12x^3 + 38x^2 + 4}\)
2. \(\color{blue}{12x^2 – 3 }\)
3. \(\color{blue}{3x^3 – 1}\)
4. \(\color{blue}{x^2 – 8x + 15}\)
5. \(\color{blue}{9x^2 – 64}\)
6. \(\color{blue}{16x^2 – 8x + 5}\)

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