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.
