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

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)

Simplify:
This gives us:
(5x + x^4)  3x^4  4x

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

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.