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In algebraic expressions, multiplication is a fundamental operation that can often be straightforward but requires a keen understanding to avoid errors. When multiplying numbers, particularly negative values, pay close attention to the signs.

* **Positive \cdot Positive:** The result is positive. * **Negative \cdot Negative:** The result is positive because the negatives cancel each other out. * **Positive \cdot Negative:** The result is negative as one sign is negative. * **Negative \cdot Positive:** Similarly, the result is negative.
In our example, there were several multiplication instances:- \(-3 \cdot 8 = -24\) - \(-5 \cdot 6 = -30\)- \(-4 \cdot 12 = -48\)- \(3 \cdot 9 = 27\)Each calculation respects the sign, ensuring accuracy in their outcome. It’s key to apply multiplication correctly by handling one pair of numbers at a time.

Subtraction is another crucial arithmetic operation needed to simplify algebraic expressions.
When simplifying expressions, subtraction often comes after multiplication in the order of operations. Pay attention to the placement of negative signs when subtracting:

• If you have two numbers with the same sign, keep the same sign and sum the numbers.
• If the signs differ, subtract and keep the sign of the larger absolute value.
• If subtracting a negative number, it is equivalent to adding the positive version of that number.

This understanding is evident in the expression: - After calculating \(-24\) from \(-3 \cdot 8\) and \(-30\) from \(-5 \cdot 6\), the subtraction \(-24 - 30 = -54\) shows how subtraction modifies the final output.- Similarly, \([2 \cdot 8] - 11\) equates to \(16 - 11 = 5\), demonstrating subtraction after multiplication. Remember to simplify bracketed expressions first and handle negative signs accurately to ensure correct outcomes.

Understanding the order of operations (often recalled by the acronym PEMDAS/BODMAS) is crucial for tackling complex expressions correctly. This order reflects:
* **Parentheses/Brackets First:** Solve anything inside parentheses or brackets first. * **Exponents/Orders:** Evaluate powers or roots next. * **Multiplication and Division:** From left to right. * **Addition and Subtraction:** Finally, from left to right.
In our exercises, this approach is evident:

• In part b, the operation inside brackets \(-2 - (-4)\) simplifies before any other calculations, following the rule to tackle parentheses first.
• Afterwards, multiplication is handled, followed by subtraction.
• In part d, we first multiply \(3 \cdot 9\) before handling subtraction and additional subtraction.

By learning and applying this logical sequence, you can navigate through expressions accurately, preventing errors commonly made by skipping or misordering the steps.