Problem 27 Simplify. $$ (11-8)^{2}-(18-... [FREE SOLUTION]

91影视

Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 1: Problem 27

Simplify. $$ (11-8)^{2}-(18-16)^{2} $$

Short Answer

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Step by step solution

Simplify Inside the Parentheses

First, simplify the expressions inside the parentheses: $ 11 - 8 = 3 $ and $ 18 - 16 = 2 $.

Square the Results

Next, square the results of the simplified expressions: $ 3^{2} = 9 $ and $ 2^{2} = 4 $.

Subtract the Squared Values

Finally, subtract the squared results: $ 9 - 4 = 5 $.

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Key Concepts

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

order of operations

To simplify any algebraic expression, it's crucial to follow the order of operations. This is a standard rule that dictates the sequence in which mathematical operations should be completed. The order can be remembered with the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Ignoring the order of operations can lead to incorrect results. By following PEMDAS, we ensure each expression is simplified accurately.
In our example, the first step involves simplifying expressions inside parentheses, then squaring the results, and finally subtracting the squared results.

parentheses

When faced with expressions within parentheses, our first task is to simplify these expressions. Parentheses indicate which operations should be performed first, as they group specific parts of an equation that need to be dealt with before other operations.
In our specific problem, we have the expressions $11 - 8$ and $18 - 16$ inside parentheses. We simplify these first to get simpler numbers to work with. Specifically, $11 - 8 = 3$ and $18 - 16 = 2$.
By addressing the parentheses first, we ensure that the subsequent operations are easier and we follow the proper mathematical conventions.

squaring numbers

Squaring a number means multiplying the number by itself. In mathematical notation, squaring is represented as an exponent of 2, such as $3^{2}$.
In our example, after simplifying the expressions inside the parentheses, we are left with the numbers 3 and 2. The next step is to square these numbers. $3^{2} = 9$ and $2^{2} = 4$.
Understanding squaring is essential because it frequently appears in algebraic expressions and solving these correctly hinges on knowing how to square numbers accurately.
Finally, after squaring each result, we can subtract them: $9 - 4 = 5$. This gives us the simplified result of the original expression.

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91影视

Simplify. $$ (11-8)^{2}-(18-16)^{2} $$

Short Answer

Step by step solution

Simplify Inside the Parentheses

Square the Results

Subtract the Squared Values

Key Concepts

order of operations

parentheses

squaring numbers

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