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When you encounter algebraic expressions like \(35xy + 12 - 110xy - 14\), the goal is to simplify them to make it easier to understand or solve related problems. Simplifying an expression means to rewrite it in a more concise way, eliminating unnecessary terms while preserving its value. In our example, simplifying commences by identifying components of the expression that can be combined. These components often involve similar or related mathematical elements termed 'like terms', which can be added or subtracted together. By focusing on each part of the expression separately, you can gradually simplify until you reach its most basic, manageable form.

Like terms are terms within an algebraic expression that have identical variable parts. Only like terms can be combined through addition or subtraction in the simplification process. For instance, in the expression \(35xy + 12 - 110xy - 14\), the terms \(35xy\) and \(-110xy\) are like terms because they both contain the variable combination \(xy\). This makes them eligible for simplification. On the other hand, the numbers \(12\) and \(-14\) stand alone without variables. Therefore, they are like terms among themselves, acting as constants, and can be combined separately. Understanding the concept of like terms is crucial as it enables you to correctly combine and reduce expressions, leading to more intuitive and simpler problems.

Combining like terms is the next step in simplifying expressions once you have identified them. It involves adding or subtracting coefficients of like terms. The coefficients are numerical values placed in front of the variables, representing how many of that particular term exists. In our exercise \(35xy + 12 - 110xy - 14\), combining the like terms \(35xy\) and \(-110xy\) results in subtraction because \(-110\) has a negative sign. So, \(35xy + (-110xy) = -75xy\). Similarly, combining the constant like terms \(12\) and \(-14\) gives \(12 + (-14) = -2\). This method of combining like terms streamlines the expression, producing a simpler expression, \(-75xy - 2\). By efficiently grouping and reducing like terms, we turn a complex expression into a straightforward one, helping us solve or interpret it more effectively.