In Exercises 42–46, simplify each algebraic expression.5x+7x²-4x+2x²

Verified step by step guidance

1. Combine like terms by identifying terms with the same variable and exponent.
2. First, look at the terms with \(x^2\): \(7x^2\) and \(2x^2\).
3. Add the coefficients of the \(x^2\) terms: \(7 + 2\).
4. Next, look at the terms with \(x\): \(5x\) and \(-4x\).
5. Add the coefficients of the \(x\) terms: \(5 - 4\).

Key Concepts

Combining Like Terms

Combining like terms is a fundamental algebraic process where terms with the same variable and exponent are added or subtracted. For example, in the expression 5x + 7x² - 4x + 2x², the like terms 5x and -4x can be combined to simplify the expression. This step is crucial for reducing expressions to their simplest form.

Polynomial Expressions

A polynomial expression is a mathematical expression that consists of variables raised to non-negative integer powers and their coefficients. In the given expression, 5x + 7x² - 4x + 2x², the terms are polynomials of degree one and two. Understanding polynomials is essential for performing operations like addition, subtraction, and simplification.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. While simplifying expressions, it is important to follow these rules, typically remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This concept helps in correctly simplifying complex expressions.