Simplifying Polynomial Expressions: (8a^5  4) + (3a^5 + a  2)
This article will guide you through the process of simplifying the polynomial expression (8a^5  4) + (3a^5 + a  2).
Understanding the Basics
Before we dive into simplification, let's refresh our understanding of some key terms:
 Polynomial: A mathematical expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, where exponents can only be nonnegative integers.
 Terms: The individual parts of a polynomial separated by addition or subtraction signs.
 Like Terms: Terms that have the same variable(s) raised to the same powers.
Simplifying the Expression

Remove parentheses: Since we are adding the two polynomials, the parentheses don't affect the order of operations.
(8a^5  4) + (3a^5 + a  2) = 8a^5  4 + 3a^5 + a  2

Combine like terms: Identify terms with the same variables and exponents.
 a^5 terms: 8a^5 + 3a^5 = 11a^5
 a terms: + a (this is the only term with 'a' to the power of 1)
 Constant terms: 4  2 = 6

Write the simplified expression: Combine the simplified terms in descending order of their exponents.
11a^5 + a  6
Conclusion
Therefore, the simplified form of the expression (8a^5  4) + (3a^5 + a  2) is 11a^5 + a  6. This process involves understanding the basic components of polynomials and combining like terms for a simplified expression.