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In algebra, a key concept is understanding and identifying 'like terms.' Like terms are terms within an expression that have identical variables raised to the same power. For instance, in the expression \((a-3)+(5-6a)\), the terms \(a\) and \(-6a\) are like terms because they both involve the variable \(a\) raised to the same power of one. Recognizing like terms is essential because it allows us to simplify expressions easily. Constant terms like \(-3\) and \(5\) are also considered like terms, even though they don’t have variables. They are simply numbers, and sharing the trait of being ‘constant’ makes them like terms as well. Identifying and grouping like terms helps one simplify expressions more efficiently.

Simplifying algebraic expressions involves rewriting them in a simpler, more condensed form without changing their value. This process often makes expressions easier to work with in further calculations. To simplify the expression \((a-3)+(5-6a)\), the first step is to identify and combine like terms.
When simplifying, it's essential to consider the operations between terms, such as addition or subtraction, and apply them carefully to like terms. The goal is to consolidate these terms to reduce the expression to its most basic form. In our example, simplifying results in \(-5a + 2\), combining the variable and constant terms into a more manageable expression.

Combining like terms involves performing basic arithmetic operations, such as addition and subtraction, on the coefficients of the like terms. In the expression \((a-3)+(5-6a)\), we start by focusing on the like terms \(a\) and \(-6a\).
- For these variable terms, look at their coefficients (the numbers in front of the variables): \(1\) for \(a\) and \(-6\) for \(-6a\). - By combining \(a - 6a\), we subtract the coefficients, resulting in \(-5a\).Next, we turn our attention to the constant terms (numbers without variables), which are \(-3\) and \(5\).
- By adding these constants together, \(-3 + 5\), we reach the result of \(2\). The expression as a whole then simplifies to \(-5a + 2\). Understanding how to combine like terms is crucial for algebraic manipulation, assisting in solving equations, and making expressions easier to work with.