%2B(-n%5E2-3n%2B11).jpeg "(2n^2-5n-6)+(-n^2-3n+11)")
Simplifying Algebraic Expressions: (2n^2 - 5n - 6) + (-n^2 - 3n + 11)
In algebra, simplifying expressions involves combining like terms to make the expression more concise and easier to understand. Let's look at the expression (2n^2 - 5n - 6) + (-n^2 - 3n + 11) and break down the steps for simplifying it.
Understanding Like Terms
Before we begin, let's define like terms:
- Like terms have the same variables raised to the same powers.
- For example, 2n^2 and -n^2 are like terms because they both have the variable 'n' raised to the power of 2.
- Similarly, -5n and -3n are like terms because they both have the variable 'n' raised to the power of 1.
Simplifying the Expression
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Remove the parentheses: Since we are adding the two expressions, the parentheses don't affect the signs of the terms inside.
- (2n^2 - 5n - 6) + (-n^2 - 3n + 11) = 2n^2 - 5n - 6 - n^2 - 3n + 11
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Combine like terms:
- n^2 terms: 2n^2 - n^2 = n^2
- n terms: -5n - 3n = -8n
- Constant terms: -6 + 11 = 5
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Write the simplified expression: The simplified form of the given expression is n^2 - 8n + 5.
Conclusion
By following these steps, we have successfully simplified the expression (2n^2 - 5n - 6) + (-n^2 - 3n + 11) to its simplest form, n^2 - 8n + 5. Remember, simplifying expressions is a fundamental skill in algebra that helps you manipulate and solve equations more efficiently.