How to Simplify Polynomials

How to Simplify Polynomials

To simplify polynomials, you need to find ‘like’ terms and combine them. Here you can learn how to simplify polynomials.

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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 – Example 1:

Simplify this expression. \(2x(2x-4)=\)

Solution:

Use Distributive Property: \(2x(2x−4)=4x^2−8x\)

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: \(7x^3+2x^3= 10x^3 \), \(2x^4-4x^4= -2x^4 \)
Now simplify and write in standard form: \(7x^3+2x^4+2x^3-4x^4-8x=-2x^4+10x^3-8x\)

Exercises for Simplifying Polynomials

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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