%2B(3a%5E5%2Ba-2).jpeg "(8a^5-4)+(3a^5+a-2)")
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 non-negative 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
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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
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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
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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.