How to Calculate (A – B)^2: Step-by-Step Guide

In mathematics, understanding how to calculate the square of the difference of two numbers, denoted as (A – B)^2, is a fundamental concept. This operation appears in various mathematical problems, equations, and formulas. In this guide, we will walk you through the step-by-step process of calculating (A – B)^2 to help you grasp the mechanics behind this operation more effectively.

Breaking Down the Formula

Before diving into the calculations, let’s break down the formula (A – B)^2. This expression represents the square of the difference between two numbers, A and B.

Expanding the expression (A – B)^2 results in:

(A – B)^2 = A^2 – 2AB + B^2

This expanded form is derived through the process of foiling or expanding a binomial squared. By following a systematic approach, we can simplify this expression to obtain the final result.

Step-by-Step Calculation Process

Now, let’s go through the step-by-step process of calculating (A – B)^2:

Step 1: Square A

• Start by squaring the value of A.
• This can be represented as A^2.

Step 2: Square B

• Proceed by squaring the value of B.
• This can be represented as B^2.

Step 3: Multiply A and B

• Multiply the values of A and B together.
• This can be represented as 2AB.

Step 4: Combine the Results

• Combine the individual results from Steps 1, 2, and 3 to form the final expression.
• The final expression of (A – B)^2 is: A^2 – 2AB + B^2.

Example Calculation

To illustrate this process, let’s consider an example with specific values for A and B:

Given: A = 5, B = 3

Step 1: Square A

• A^2 = 5^2 = 25

Step 2: Square B

• B^2 = 3^2 = 9

Step 3: Multiply A and B

• 2AB = 2 * 5 * 3 = 30

Step 4: Combine the Results

• (A – B)^2 = A^2 – 2AB + B^2 = 25 – 30 + 9 = 4

Therefore, the square of the difference between 5 and 3 is 4.

FAQs

Q1: What does (A – B)^2 represent?

• A1: (A – B)^2 represents the square of the difference between two numbers, A and B.

Q2: Why is it essential to understand (A – B)^2?

• A2: Understanding (A – B)^2 is crucial in various mathematical calculations and problem-solving scenarios.

Q3: Can (A – B)^2 be negative?

• A3: Yes, the result of (A – B)^2 can be negative, zero, or positive depending on the values of A and B.

Q4: What is the significance of each term in the expanded form of (A – B)^2?

• A4: In the expansion A^2 – 2AB + B^2, the terms represent the squares of A and B, and the product of A and B, respectively.

Q5: How can (A – B)^2 be applied in real-life situations?

• A5: (A – B)^2 finds applications in areas such as physics, engineering, finance, and computer science for calculating differences or variances.

By mastering the steps outlined in this guide, you can confidently calculate (A – B)^2 and leverage this knowledge across various mathematical contexts. Stay tuned for more in-depth guides on mathematical concepts and operations.