%2B(5n%5E2%2B2).jpeg "(4+2n^3)+(5n^2+2)")
Simplifying Algebraic Expressions: (4 + 2n^3) + (5n^2 + 2)
This article will explore the simplification of the algebraic expression (4 + 2n^3) + (5n^2 + 2). We will break down the process step by step to understand how to combine like terms and arrive at the simplified form.
Understanding the Expression
The expression consists of two sets of terms enclosed in parentheses:
- (4 + 2n^3): This set includes a constant term (4) and a term with a variable raised to the third power (2n^3).
- (5n^2 + 2): This set includes a term with a variable raised to the second power (5n^2) and a constant term (2).
Combining Like Terms
To simplify the expression, we need to combine terms that have the same variable and exponent.
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Identify like terms:
- Constant terms: 4 and 2
- Terms with n^3: 2n^3 (there is no other term with n^3)
- Terms with n^2: 5n^2 (there is no other term with n^2)
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Combine like terms:
- 4 + 2 = 6
- 2n^3 + 0 = 2n^3
- 5n^2 + 0 = 5n^2
Simplified Expression
By combining the like terms, we arrive at the simplified expression: 2n^3 + 5n^2 + 6
Conclusion
Simplifying algebraic expressions involves identifying like terms and combining them through addition or subtraction. In this case, we successfully combined the terms in the expression (4 + 2n^3) + (5n^2 + 2) to obtain the simplified form 2n^3 + 5n^2 + 6. This process is crucial for solving equations, simplifying formulas, and understanding mathematical relationships.