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.

Remove the parentheses: Since we are adding the terms inside the parentheses, we can simply remove them: x + 2x² + 4x² + 7x

Combine like terms: Combine the linear terms (x and 7x) and the quadratic terms (2x² and 4x²): (x + 7x) + (2x² + 4x²)

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.