Simplifying Polynomial Expressions: (5x^3+7x8)+(2x^35x^2x)
This article will guide you through the process of simplifying the polynomial expression: (5x^3+7x8)+(2x^35x^2x).
Understanding the Basics
Before we dive into the simplification, let's review some fundamental concepts about polynomials:
 Polynomials: Expressions involving variables with nonnegative integer exponents, combined with constants, using addition, subtraction, and multiplication.
 Terms: Individual parts of a polynomial separated by plus or minus signs.
 Like Terms: Terms that have the same variable and exponent.
Simplifying the Expression

Remove the Parentheses: Since we're adding polynomials, the parentheses don't affect the order of operations. We can simply remove them:
(5x^3 + 7x  8) + (2x^3  5x^2  x) = 5x^3 + 7x  8 + 2x^3  5x^2  x

Combine Like Terms: Identify and group terms with the same variable and exponent:
 x^3 terms: 5x^3 + 2x^3 = 7x^3
 x^2 terms: 5x^2
 x terms: 7x  x = 6x
 Constant terms: 8

Write the Simplified Expression: Combine all the like terms to get the simplified expression:
7x^3  5x^2 + 6x  8
Conclusion
Therefore, the simplified form of the polynomial expression (5x^3+7x8)+(2x^35x^2x) is 7x^3  5x^2 + 6x  8. Remember, combining like terms is the key to simplifying polynomial expressions.