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Simplifying expressions involves breaking down math problems into simpler parts to make them easier to solve. Performing operations in the right order is essential for arriving at the correct answer. This is why we use a specific set of rules known as the order of operations.

• Start by dealing with any expressions inside parentheses.
• Next, handle exponents, if there are any.
• Then, look at multiplication and division from left to right.
• Lastly, address addition and subtraction from left to right.

This order can be remembered with the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Following these steps ensures accuracy when simplifying complex expressions. In our given problem, simplifying the expression started with the operations inside parentheses, followed by multiplication, and then addition and subtraction.

Parentheses help make math expressions clearer by grouping parts of an equation that should be solved first. This is vital because parentheses can change the outcome of calculations. For example, consider our expression: \[ 2(14+3)-8 \cdot 2+(9-2) \]Parentheses appear around \((14+3)\) and \((9-2)\). According to the order of operations, these additions and subtractions inside the parentheses need to be calculated first, transforming our expression into:\[ 2(17) - 8 \cdot 2 + 7 \]By handling what's in the parentheses first, we simplify the equation accurately before moving to other operations like multiplication. Always prioritize operations in parentheses to ensure that calculations are simplifying correctly and following mathematical conventions.

Addition and subtraction can be tricky if not handled in the right sequence. They are often the last operations to be performed when simplifying expressions. According to the order of operations, addition and subtraction should be processed from left to right, just like reading a book. After addressing parentheses and solving any multiplication or division problems, tackle the addition and subtraction:Starting from left to right:\[ 34 - 16 + 7 \]First, subtract 16 from 34, resulting in 18. Then, add 7:\[ 18 + 7 = 25 \]By following the left-to-right rule, we ensure that each step leads correctly to the final simplified answer. Ignoring this sequence may lead computational errors. Being attentive to this detail can significantly help in solving expressions correctly.