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Algebraic expressions are mathematical statements that consist of numbers, variables, and arithmetic operations like addition, subtraction, multiplication, and division. These expressions can represent real-life situations and can be manipulated through various operations. For example, the expression \(3x^2 + 4x - 5\) consists of:

• Coefficients: Numbers like 3, 4, and -5 that are multiplied by the variables or stand-alone.
• Variables: Symbols such as \(x\) that represent unknown values.
• Exponents: In terms like \(3x^2\), the exponent (2) represents how many times the variable is multiplied by itself.

Algebraic expressions can be combined and simplified through operations including addition, subtraction, and distribution. Understanding how to manipulate these expressions is fundamental in algebra, allowing students to solve equations and understand complex mathematical relationships.

Like terms are terms that include the same variable raised to the same power. Recognizing like terms is crucial in simplifying algebraic expressions, especially when performing operations like addition or subtraction. For instance, in the expressions \(3x^2 + 4x - 5\) and \(-2x^2 - 2x + 3\):

• \(3x^2\) and \(-2x^2\) are like terms because they both contain \(x^2\).
• \(4x\) and \(-2x\) are also like terms as they both have the variable \(x\) to the first power.
• The constants \(-5\) and \(3\) are like terms as they are just numbers without variables.

Identifying like terms allows you to effectively combine them, simplifying the expression to its most elementary form. This is key to ensuring that algebraic expressions are as simple as possible for further manipulation or interpretation.

Simplifying expressions involves reducing them to their simplest form by combining like terms and performing arithmetic operations. The goal is to make the expression as compact and understandable as possible, which often makes problem-solving more straightforward.In the given exercise:- Start with identifying like terms.- Apply subtraction to each pair of like terms: perform \(3x^2 - (-2x^2)\), \(4x - (-2x)\), and \(-5 - 3\).- Remember, subtracting a negative is the same as adding the positive equivalent. For example, \(3x^2 - (-2x^2)\) is equivalent to \(3x^2 + 2x^2 = 5x^2\).This method results in a simplified form \(5x^2 + 6x - 8\), showcasing how subtraction and thoughtful arithmetic lead to a cleaner, more manageable expression. Simplifying expressions is a fundamental skill in algebra that helps ensure that you can easily interpret and use equations in various contexts.