(4a^4-6a^3-3a^2+a+1)+(5a^3+7a^2+2a-2)

3 min read Jun 16, 2024

Adding Polynomials: A Step-by-Step Guide

This article will guide you through the process of adding the polynomials (4a^4-6a^3-3a^2+a+1) and (5a^3+7a^2+2a-2).

Before we start adding, let's understand what polynomials are:

Polynomials are expressions made up of variables and constants, combined using addition, subtraction, and multiplication.
Terms are the individual parts of a polynomial separated by plus or minus signs.
Like terms have the same variable and the same exponent.

Write the polynomials in a vertical format. Align the terms with the same variables and exponents.
```
4a^4 - 6a^3 - 3a^2 + a  + 1
+ 5a^3 + 7a^2 + 2a - 2
------------------------
```
Add the coefficients of like terms. Remember that if a term doesn't have a coefficient, it is understood to be 1.
```
4a^4 - 6a^3 - 3a^2 + a  + 1
+ 5a^3 + 7a^2 + 2a - 2
------------------------
4a^4 - 1a^3 + 4a^2 + 3a - 1 
```
Simplify the result.

The final simplified sum of the polynomials is 4a^4 - a^3 + 4a^2 + 3a - 1.

Combining Like Terms: The core of adding polynomials lies in combining like terms.
Vertical Format: Writing polynomials vertically makes it easier to identify and combine like terms.
Order Matters: While you can rearrange terms, it's generally helpful to maintain a descending order of exponents for clarity.

By following these steps, you can successfully add any polynomials, no matter how complex they may seem.