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

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (6x-2x^3+1)-(7x^2-5-4x^3)

This article will guide you through the process of simplifying the polynomial expression: (6x-2x^3+1)-(7x^2-5-4x^3). We'll break down each step to ensure a clear understanding.

Understanding the Basics

Before we start simplifying, let's define some key terms:

• Polynomial: An expression consisting of variables and constants, combined using addition, subtraction, and multiplication, where the variables have non-negative integer exponents.
• Term: A single part of a polynomial separated by addition or subtraction.
• Coefficient: The numerical factor in front of a variable.
• Like Terms: Terms with the same variables raised to the same exponents.

Simplifying the Expression

1. Distribute the Negative Sign: The minus sign in front of the parentheses means we multiply each term inside the second set of parentheses by -1:

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

   This gives us:

   6x - 2x^3 + 1 - 7x^2 + 5 + 4x^3
   

2. Combine Like Terms: Now we identify terms with the same variables and exponents:

   • x^3 terms: -2x^3 + 4x^3 = 2x^3
   • x^2 terms: -7x^2
   • x terms: 6x
   • Constant terms: 1 + 5 = 6

3. Write the Simplified Expression: Combining the like terms, we get:

   2x^3 - 7x^2 + 6x + 6
   

Final Result

The simplified form of the expression (6x-2x^3+1)-(7x^2-5-4x^3) is 2x^3 - 7x^2 + 6x + 6.

By following the steps outlined above, you can confidently simplify any polynomial expression involving addition, subtraction, and parentheses.