# How to Simplify 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.

### 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. $$\color{blue}{(8x^2 – 3x) – (5x – 5 – 8x^2)}$$

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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