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Simplifying algebraic expressions involves breaking down a complex equation into its simplest form. This makes it easier to work with and understand. The primary goal is to reduce the expression to a form where all similar terms are combined, and unnecessary parts are removed. This simplification process involves a few important steps:

• Distribute coefficients: Use the distributive property to clear parentheses.
• Simplify terms: Compute simple arithmetic to clean up individual terms.
• Combine like terms: Gather and merge all similar factors.

Taking these steps results in a clearer and more concise expression. It’s crucial in both solving equations and understanding their behavior.

The distributive property is a fundamental rule in algebra that allows you to multiply a single term by a sum or difference contained in parentheses. The rule can be expressed as: - For any numbers or variables, \( a(b + c) = ab + ac \) or \( a(b - c) = ab - ac \).This property is very useful when you encounter expressions with parentheses, as it lets you eliminate them by distributing, or spreading, the multiplication over all terms inside. For example, consider the expression \( -2(x + 4) \). You would multiply - \(-2\times x = -2x\) - \(-2\times 4 = -8\)This method ensures that each term inside the parentheses is multiplied individually by the term outside, helping to simplify the entire expression.

Once you have distributed terms across parentheses, the next step in simplification is combining like terms. "Like terms" refer to terms that have the same variable raised to the same power, or are constants. Here's how you can identify and combine them:

• Identify terms with the same variable and exponent. For example, \(-2x\) and \(24x\) are like terms because they both contain \(x\).
• Add or subtract the coefficients of these terms. With \(-2x + 24x\), you simply perform the arithmetic on the coefficients \(-2 + 24\) to obtain \(22x\).
• Combine constant terms by adding or subtracting them. For instance, in the expression \(-8 - 8\), you calculate to get \(-16\).

Combining like terms is an essential step to ensure that the final expression is as simple and easy to interpret as possible, leading to results like \(22x - 16\). This makes further calculations and insights much more straightforward.