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The order of operations is crucial to solving algebraic expressions correctly. It ensures that everyone interprets and solves an expression in the same way. The sequence everyone should follow can be remembered by the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In the exercise provided, each calculation begins with multiplication before moving on to addition or subtraction. This is consistent with the order of operations where multiplication and division take precedence over addition and subtraction. Following this order without deviations ensures accurate results, especially when expressions become more complex.

Working with negative numbers can trip up many students because it changes the basic operations we are used to. A negative number is less than zero, and understanding how to manipulate them in equations is an essential skill.
When multiplying two numbers, a negative number multiplies with another negative to produce a positive result (e.g., \((-2) imes (-6) = 12\)). Meanwhile, a negative times a positive remains negative (e.g., \(5 imes (-4) = -20\)).
Adding and subtracting negative numbers also requires caution. For instance, adding a negative number is akin to subtraction (e.g., \(3 + (-28) = 3 - 28 = -25\)). Hence, mastering these concepts enables you to handle real-world situations involving debts or losses effectively.

Multiplication in algebra isn't vastly different from arithmetic multiplication. However, it often involves variables and more complex expressions.Multiplicands can include both constants (numbers) and variables, and the processes followed still adhere to the normal rules of arithmetic. The basic concept often involves combining like terms and applying known operations such as distributive, associative, and commutative properties for simplification.
In the given exercise, multiplication is handled by taking each number and its operations. For instance, recognizing that \((-5) imes 3\) truly means taking five groups of negative three. Moreover, multiplying to simplify within parentheses before addressing any addition or subtraction enhances clarity and accuracy.Understanding multiplication in algebra forms the cornerstone of solving equations and polynomials, expanding your capacity to tackle complex problems.

Parentheses in algebra are vital for dictating the order in which operations are performed. They act as a signaling tool that certain operations needed to be resolved first. This can change the outcome significantly if overlooked.
For example, in the expression \((-3-5)\cdot -2\), the operations inside the parentheses \((-3-5)\) are completed first, resulting in \(-8\), which is then multiplied by \(-2\). Ignoring parentheses or misinterpreting their placement can lead to wrong results.
In scenarios involving nested parentheses, you address operations from the innermost to the outermost, making sure not to skip any step.The use of parentheses provides clarity and precision in calculations, helping to organize expressions in ways that are straightforward and efficient to solve.