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

3 min read Jun 16, 2024
(4a^4-6a^3-3a^2+a+1)+(5a^3+7a^2+2a-2)

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).

Understanding Polynomials

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.

Adding Polynomials: The Process

  1. 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
    ------------------------
    
  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 
    
  3. Simplify the result.

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

Key Takeaways

  • 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.

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