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Simplifying algebraic expressions is all about making an expression easier to work with. This involves reducing it to its simplest form without changing its value. In the context of algebra, to "simplify" an expression means to:

• Remove parentheses by distributing any coefficients.
• Combine similar terms to create fewer terms.
• Simplify any fractions or ratios, if applicable.

Consider the algebraic expression \(-2(5x + 5)\). To simplify this, we will apply two main techniques: coefficient distribution and combining like terms. By doing this, the expression becomes easier to interpret and solve in larger algebraic problems. Simplifying expressions is a foundational skill in algebra, providing clarity and efficiency in computation.

Coefficient distribution, often referred to as the distributive property, involves multiplying a single term (the coefficient) with each term inside a set of parentheses. This method is essential in simplifying expressions, particularly when dealing with polynomials.In our example, the expression \(-2(5x + 5)\) involves distributing the \(-2\) across both terms inside the parentheses:

• Multiply \(-2\) by \(5x\) to get \(-10x\)
• Multiply \(-2\) by \(+5\) to get \(-10\)

Each term inside the parentheses has been individually multiplied by the coefficient, \(-2\). This results in a new expression that can be simplified further. Coefficient distribution ensures each part of the expression is correctly accounted for and is a critical step in maintaining the integrity of algebraic equations.

Once the expression has undergone distribution, the next step is to combine like terms. Like terms are terms that have identical variable parts.For instance, in the expression \(-10x - 10\), the terms cannot be combined further in terms of like terms because:- \(-10x\) and \(-10\) are not like terms; one is a variable term and the other is a constant.Combining like terms involves:

• Adding or subtracting coefficients of terms with the same variable.
• Combining constant numbers together.

Although our initial expression simplifies directly to \(-10x - 10\) without further need to combine like terms, knowing how to do so is important for more complex expressions. This step reduces complexity and provides a clear and concise form of the expression, ultimately facilitating problem solving in algebra.