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Simplifying Algebraic Expressions: (x + 2x²) + (4x² + 7x)
This article will guide you through the process of simplifying the algebraic expression (x + 2x²) + (4x² + 7x).
Understanding the Expression
The expression consists of two sets of terms enclosed in parentheses. Let's break down the terms:
- x: This is a linear term (power of 1).
- 2x²: This is a quadratic term (power of 2).
- 4x²: This is another quadratic term.
- 7x: This is another linear term.
Simplifying the Expression
To simplify the expression, we need to combine like terms. Like terms have the same variable raised to the same power.
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Remove the parentheses: Since we are adding the terms inside the parentheses, we can simply remove them: x + 2x² + 4x² + 7x
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Combine like terms: Combine the linear terms (x and 7x) and the quadratic terms (2x² and 4x²): (x + 7x) + (2x² + 4x²)
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Simplify: 8x + 6x²
Final Answer
The simplified form of the expression (x + 2x²) + (4x² + 7x) is 8x + 6x².
Key Takeaways
- Like terms: Terms with the same variable raised to the same power can be combined.
- Order of operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.
- Combining terms: When combining like terms, only add the coefficients (numbers in front of the variables).
By understanding these principles, you can confidently simplify various algebraic expressions.