Simplifying Polynomials

Simplifying Polynomials

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

Example 1:

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

Solution:

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

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

Example 3:

Simplify this expression. \(4x(6x-3)=\)

Solution:

Use Distributive Property: \(4x(6x-3)=24x^2-12x\)

Example 4:

Simplify this expression. \(7x^3+2x^4+2x^3-4x^4-8x=\)

Answer:

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

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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