91Ó°ÊÓ

In algebra, simplifying expressions is crucial, and one essential skill for this is combining like terms. This means finding and merging terms in an expression that have identical variable parts. Like terms have variables raised to the same power. For example, in the expression \(15x - 4 + 6x - 9\), the like terms are \(15x\) and \(6x\) because both have the variable \(x\).When combining like terms, you focus on the coefficients—the numbers in front of the variables. By adding the coefficients of \(15x\) and \(6x\), which are 15 and 6, the result is \(21x\). By simplifying the expression step by step, you ensure clarity and correctness of your solution. Breaking down expressions into like terms first often makes complex problems much simpler to handle.

A vital part of working with algebraic expressions is identifying coefficients. The coefficients are the numbers placed directly in front of variables, acting as multipliers. Recognizing them is key to simplifying expressions effectively.In the expression \(15x - 4 + 6x - 9\), the coefficients are 15 from \(15x\) and 6 from \(6x\). These numbers tell us how many times the variable \(x\) is being added together. By focusing on coefficients, you can accurately combine like terms. Properly handling coefficients makes algebraic operations straightforward and prevents errors during simplification.

Constant terms in an algebraic expression are the numbers that stand alone, without attached variables. They are called "constant" because their values do not change; they remain fixed in value.For instance, in \(15x - 4 + 6x - 9\), \(-4\) and \(-9\) are constant terms. You can think of them as everyday numbers within algebra. When simplifying, add or subtract these constants just like basic arithmetic: \(-4 + (-9) = -13\). Understanding constant terms helps ensure you appropriately adjust the expression by handling numbers correctly, ultimately reaching a cleaner, simplified result.