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When simplifying algebraic expressions, identifying 'like terms' is crucial. Like terms are terms that have the same variables raised to the same power. For example, in the expression \(19a + 44 - 19a\), '19a' and '-19a' are like terms because they both contain the variable 'a'. Like terms can also include constants, which are just numbers without variables. Identifying these terms correctly helps in the simplification process by ensuring that you only combine terms that are truly comparable.

Once you've identified like terms, the next step is to combine them. In algebra, this often means adding or subtracting the coefficients (the numerical parts of the terms) while keeping the variable part the same. For the expression \(19a + 44 - 19a\), you combine '19a' and '-19a' by subtracting them: \(19a - 19a = 0a\). This simplifies to 0. The constant term, 44, stays as it is. When combining like terms, always perform the operations (addition or subtraction) indicated and then rewrite the algebraic expression with the simplified terms.

Simplifying an algebraic expression involves several straightforward steps. Here is a breakdown:

1. **Identify Like Terms:** Look at the expression and find terms with the same variables and exponents. For example, \(19a\) and \(-19a\) are like terms.
2. **Combine Like Terms:** Perform the addition or subtraction on the coefficients of like terms. Using the expression \(19a - 19a\) leaves us with 0. The constants or any other terms that are not alike should be left as they are.
3. **Write the Final Simplified Expression:** After combining all like terms, write down the new simplified expression. In this case, the expression \(19a + 44 - 19a\) simplifies to just 44. An important note is that the variable terms canceled each other out, leaving only the constant term.

Simplifying expressions by following these steps makes the process more systematic and ensures accuracy.