what is the simplified form of the following expression assume

Guri Bee

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22-10-2024

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Simplifying Expressions: A Step-by-Step Guide

Simplifying expressions is a fundamental skill in algebra and other branches of mathematics. It involves rewriting complex expressions in a more concise and manageable form. This article explores how to simplify expressions, using examples and explanations inspired by questions and answers found on GitHub.

Understanding the Concept:

The goal of simplifying an expression is to reduce it to its most basic form while maintaining its original value. This often involves combining like terms, applying the order of operations (PEMDAS/BODMAS), and using algebraic properties.

Example from GitHub:

Question: What is the simplified form of the following expression, assuming all variables are non-zero?

(x^2 + 2xy + y^2) / (x + y)

Answer:

(x + y)^2 / (x + y) = x + y

Explanation:

The numerator of the expression is a perfect square trinomial: (x + y)^2. By factoring the numerator, we can cancel out the common factor (x + y) in both the numerator and denominator, leaving us with the simplified expression x + y.

Key Concepts in Simplifying Expressions:

• Factoring: Breaking down an expression into its constituent factors. This is crucial for identifying common factors that can be cancelled out.
• Order of Operations: Following the order of operations (PEMDAS/BODMAS) ensures calculations are performed correctly.
• Combining Like Terms: Combining terms with the same variable and exponent. For example, 3x + 2x = 5x.

Additional Examples:

1. Simplify the expression: 3(x + 2) - 2(x - 1)

   • Distribute: 3x + 6 - 2x + 2
   • Combine like terms: x + 8

2. Simplify the expression: (2x^2 + 4x) / 2x

   • Factor out a 2x from the numerator: 2x(x + 2) / 2x
   • Cancel out the common factor 2x: x + 2

Practical Applications:

Simplifying expressions is essential in various fields, including:

• Engineering: Solving equations and analyzing circuits
• Finance: Calculating interest and investments
• Computer Science: Writing algorithms and optimizing code

Conclusion:

Simplifying expressions is a fundamental mathematical skill with wide-ranging applications. Understanding the concepts of factoring, order of operations, and combining like terms can help you efficiently manipulate expressions and arrive at their simplified forms.