%2B(-3a%5E2%2B3a-1)-(a%5E2-1).jpeg "(3a^2-a+2)+(-3a^2+3a-1)-(a^2-1)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
In mathematics, simplifying expressions is a fundamental skill. It involves combining like terms and reducing the complexity of an expression. Today, we'll focus on simplifying the expression:
(3a² - a + 2) + (-3a² + 3a - 1) - (a² - 1)
Understanding the Steps
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Removing Parentheses: Start by removing the parentheses, remembering to distribute any negative signs:
(3a² - a + 2) + (-3a² + 3a - 1) - (a² - 1) = 3a² - a + 2 - 3a² + 3a - 1 - a² + 1
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Combining Like Terms: Identify terms with the same variable and exponent.
- a² terms: 3a² - 3a² - a² = -a²
- a terms: -a + 3a = 2a
- Constant terms: 2 - 1 + 1 = 2
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Final Result: Combine the simplified terms to get the final simplified expression:
-a² + 2a + 2
Key Takeaways
- Distributing Negatives: Remember to distribute negative signs when removing parentheses.
- Combining Like Terms: Only combine terms with the same variable and exponent.
- Simplifying Expressions: This process streamlines the expression, making it easier to analyze and use in further calculations.
By following these steps, you can confidently simplify algebraic expressions and gain a deeper understanding of their underlying structure.