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Prealgebra is a foundational mathematical discipline that helps students build the basic skills they need for algebra and beyond. It includes arithmetic, basic number operations, and introduces basic concepts and principles needed to solve algebraic problems.
In this exercise, we're focusing on simplifying an expression through basic operations. Prealgebra teaches you essential skills like:

• Understanding numbers and their properties
• Performing arithmetic operations (addition, subtraction, multiplication, and division)
• Working with simple expressions and equations

When you simplify expressions in prealgebra, you break them down into their simplest form so they are easier to work with in further calculations or problem-solving scenarios.

A step-by-step solution breaks down the problem into manageable parts, making it easier to understand and solve. This method ensures that each part of the problem is addressed individually and in sequence. Here's how we applied it to simplify the expression \( (8-15)(9-3) \) in our original problem.
Step 1: Simplify inside the parentheses:
Look at each set of parentheses and perform the operations inside them first. For \( (8 - 15) \), we subtract 15 from 8, which gives us -7. For \( (9 - 3) \), we subtract 3 from 9, which gives us 6. So now, our expression looks like this: \( -7 \times 6 \).
Step 2: Multiply the results:
Now take the simplified results from Step 1 and multiply them together: \[ -7 \times 6 = -42 \]
By breaking it down into these clear steps, it becomes much easier to follow and solve the problem correctly.

Multiplication is a fundamental arithmetic operation that combines groups of equal size. In this context, multiplication helps us combine the results of simplifying expressions inside parentheses. When multiplying numbers, especially with mixed signs (positive and negative), follow these rules:

• Multiplying two positive numbers gives a positive result
• Multiplying two negative numbers also gives a positive result
• Multiplying one positive and one negative number gives a negative result

So in the given exercise, \[ -7 \times 6 = -42 \], the result is negative because we are multiplying a negative number (-7) by a positive number (6).
Understanding these rules is crucial as they will help you correctly navigate through more complex problems in both prealgebra and beyond.