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Chapter 1: Problem 288

Simplify each expression. $$ (6-11)(8-13) $$

Short Answer

Expert verified
25

Step by step solution

01

Identify the values in each bracket

First, look at the values inside the brackets: \(6-11\) and \(8-13\).
02

Perform the subtraction in each bracket

Calculate the result of each subtraction: \(6 - 11 = -5\) and \(8 - 13 = -5\).
03

Multiply the results

Multiply the results obtained from the subtractions: \(-5 \times -5 = 25\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Bracket Operations
When faced with an algebraic expression enclosed in parentheses or brackets, the first step is to deal with the operations inside these brackets. This is essential because brackets indicate that the expression within them should be treated as a single unit.

For example, in the problem \( (6-11)(8-13) \), you have two sets of brackets containing subtraction operations.

Here are the steps to handle bracket operations effectively:
  • Identify the values: Look at what's inside each bracket. In this case, we have \( 6-11 \) and \( 8-13 \).

  • Perform the operations: Follow the specific operation inside the brackets. Here, it's subtraction: \( 6-11 \) and \( 8-13 \). Handle each bracket separately before combining the results.
Once you've simplified the expressions inside the brackets, you can move on to the next steps.
Subtraction
Subtraction is the process of finding the difference between two numbers. When performing algebraic subtraction, it is important to apply the correct sign rules to ensure accurate results.

Let's break down the subtraction steps in the given problem:
  • Subtraction 1 (\(6-11\)): When you subtract a larger number from a smaller number, the result is negative. Thus, \( 6-11 = -5 \).
  • Subtraction 2 (\(8-13\)): Similarly, subtracting 13 from 8 yields a negative result: \( 8-13 = -5 \).
It鈥檚 crucial to note the negative results because they will influence the next step of the problem. Remember that subtracting a larger number from a smaller one results in a negative value.
Multiplication of Negative Numbers
When multiplying numbers, the signs of the numbers determine the sign of the product. This is especially significant when dealing with negative numbers.
  • Rule 1: Positive 脳 Positive = Positive
  • Rule 2: Positive 脳 Negative = Negative
  • Rule 3: Negative 脳 Negative = Positive
In the given problem, after performing the subtractions, we are left with \( -5 \times -5 \). According to Rule 3, multiplying two negative numbers results in a positive number. Hence, \( -5 \times -5 = 25 \).

Understanding these rules will make it easier to handle expressions involving negative numbers in multiplication.

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