(5x+x^4)-(3x^4+4x)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (5x + x^4) - (3x^4 + 4x)

This article will walk through the steps of simplifying the algebraic expression: (5x + x^4) - (3x^4 + 4x).

Understanding the Expression

Before we begin, let's break down the expression:

• (5x + x^4) and (3x^4 + 4x) are both polynomials.
• Polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
• We are asked to subtract the second polynomial from the first.

Simplifying the Expression

1. Distribute the negative sign:

   The minus sign in front of the second polynomial means we need to multiply each term inside the parentheses by -1:

   (5x + x^4) + (-1)(3x^4 + 4x)

2. Simplify:

   This gives us:

   (5x + x^4) - 3x^4 - 4x

3. Combine like terms:

   Identify terms with the same variable and exponent. We can rearrange the terms to group like terms:

   x^4 - 3x^4 + 5x - 4x

4. Simplify further:

   Combine the coefficients of the like terms:

   -2x^4 + x

Final Answer

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