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Combining like terms is an essential skill in algebra that helps simplify expressions. In mathematics, terms are considered 'like' if they contain the same variables raised to the same power, differing only in their coefficients. For example, variables like \( \sqrt{17x} \) in the expression \( 6\sqrt{17x} - 8\sqrt{17x} \) are considered like terms because they carry the same radical and variable parts, differing only by their coefficients (6 and -8 respectively). The aim is to perform arithmetic operations on these coefficients while keeping the variable part unchanged.

When combining like terms, the process is straightforward:

• Identify the like terms.
• Take note of their coefficients.
• Use basic arithmetic operations (addition or subtraction) on these coefficients.

In our example, the coefficients 6 and -8 are combined by subtraction to simplify the expression, resulting in \( -2\sqrt{17x} \). This reduces complexity and helps in further mathematical operations.

Simplifying expressions is all about making mathematical phrases easier to understand or work with, while ensuring the expression remains equivalent to the original. This process often involves several techniques such as combining like terms, factoring, or reducing fractions. The most common step in simplifying is combining like terms, as seen in the initial example.

To simplify an expression like \( 6\sqrt{17x} - 8\sqrt{17x} \), we:

• Identify like terms, which here means noticing they both have the radical \( \sqrt{17x} \).
• Subtract the coefficients (6 and 8) to find the new coefficient (-2).
• Reattach the common radical to the simplified coefficient, leading to \( -2\sqrt{17x} \).

These steps reduce the expression to a simple form, making it more manageable for further calculations or analyses. Effective expression simplification can transform algebraic challenges into more accessible tasks, often revealing patterns or solutions.

An algebraic expression is a combination of numbers, variables, and operations (such as addition, subtraction, multiplication, and sometimes division). They form the backbone of algebra and can represent real-world phenomena in mathematical form. Each part of an algebraic expression, such as constants (fixed numbers) and variables (symbols standing in for numbers), plays a crucial role.

Consider the expression \( 6\sqrt{17x} - 8\sqrt{17x} \) from our example:

• Here, \( \sqrt{17x} \) includes both a constant (17) inside the radical and a variable (x).
• The operation (\