Problem 26 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ (10-1)^{2} $$

Step-by-Step Solution

Answer

81

Step 1: Simplify Inside the Parentheses

First, simplify the expression inside the parentheses: \(10 - 1\). Calculate the result of the subtraction.

Step 2: Calculate the Subtraction

Perform the subtraction: \(10 - 1 = 9\)

Step 3: Square the Result

Square the result obtained from the subtraction: \(9^{2}\). Calculate the square of 9.

Step 4: Final Calculation

Complete the operation: \(9^{2} = 81\)

Key Concepts

Order of Operations

When evaluating algebraic expressions, it’s essential to follow the order of operations. This is often remembered by the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

In the exercise \( (10-1)^2 \), we start by addressing the parentheses to simplify the expression inside them. Ensuring the correct order prevents mistakes and leads to the right answer.

Simplification

Simplification is the process of reducing an expression into its simplest form. Here, the expression inside the parentheses is \( 10 - 1 \).
To simplify:

• Perform subtraction: \( 10 - 1 = 9 \).

Simplifying expressions inside parentheses first is crucial, as seen in the order of operations.

Squaring Numbers

Squaring a number means multiplying the number by itself. In our exercise:

• After simplifying \( 10 - 1 = 9 \), we need to square 9.
• To square 9: \( 9^2 = 9 \times 9 = 81 \).

Understanding how to square numbers helps in simplifying more complex mathematical expressions.

Basic Arithmetic

Basic arithmetic includes addition, subtraction, multiplication, and division. In this problem, we focus on subtraction and multiplication.:

• Subtraction: \(10 - 1 = 9\)
• Multiplication for squaring: \(9 \times 9 = 81\)

Mastering these simple operations allows one to handle more advanced math problems easily.