Do you often find yourself struggling with algebraic expressions and equations? Are you looking for a comprehensive guide to understanding and simplifying complex mathematical formulas? If so, you’re in the right place. In this blog post, we will delve into the expanded form of (A+B-C)² and provide you with a step-by-step guide to simplify this algebraic expression.
Understanding the Algebraic Expression
Before we dive into the simplification process, let’s first understand the components of the algebraic expression (A+B-C)². This expression consists of three terms: A, B, and C. The operation being performed is addition and subtraction, along with the exponentiation of ².
Step-by-Step Simplification Process
To expand and simplify the expression (A+B-C)², we need to follow a series of steps to remove the brackets and perform the necessary operations. Let’s break down the process into manageable steps:
Step 1: Expand the Square
The first step is to expand the square of the expression. To do this, we apply the formula (x+y)² = x² + 2xy + y². In our case, x = A, y = B-C. Therefore, the expansion of (A+B-C)² is:
(A+B-C)² = A² + 2A(B-C) + (B-C)²
Step 2: Simplify the Terms
Next, we simplify the terms by expanding the expressions within the brackets. This results in:
(A+B-C)² = A² + 2AB – 2AC + B² – 2BC + C²
Step 3: Combine Like Terms
Finally, we combine the like terms to further simplify the expression:
(A+B-C)² = A² + B² + C² + 2AB – 2AC – 2BC
Conclusion
In conclusion, the expanded form of (A+B-C)² is A² + B² + C² + 2AB – 2AC – 2BC. By following the step-by-step simplification process outlined above, you can easily expand and simplify complex algebraic expressions.
Frequently Asked Questions (FAQs)
1. What is the expanded form of (A+B)²?
The expanded form of (A+B)² is A² + 2AB + B².
2. How do you simplify (3x-2y+5)²?
To simplify (3x-2y+5)², follow the same steps as outlined for (A+B-C)² by expanding the square, simplifying the terms, and combining like terms.
3. Can you explain the concept of exponentiation in algebra?
Exponentiation in algebra refers to raising a number or variable to a certain power or exponent. For example, x² represents x raised to the power of 2.
4. Are there any shortcuts or tricks to simplify algebraic expressions quickly?
Practice and familiarity with algebraic rules and formulas can help speed up the simplification process. Additionally, using online tools or calculators can aid in simplifying complex expressions efficiently.
5. How can I improve my algebra skills?
Consistent practice, solving a variety of algebraic problems, seeking help from tutors or online resources, and understanding the underlying concepts are key to improving your algebra skills.
