What is the simplified expression for the expression below? This question lies at the heart of algebraic simplification, a fundamental skill in mathematics. Understanding how to simplify expressions empowers us to solve complex equations, manipulate algebraic functions, and gain a deeper understanding of mathematical concepts.

This comprehensive guide delves into the intricacies of expression simplification, providing a step-by-step approach to mastering this essential technique. We will explore the key principles of algebraic simplification, analyze real-world examples, and uncover the power of simplifying complex expressions.

What is the Simplified Expression for the Expression Below?

To simplify an expression, we must first understand its key components and the mathematical operations involved.

Key Expression Analysis

• The given expression is: 3x + 2y – 5x + 7y
• It involves the mathematical operations of addition (+) and subtraction (-).

Simplification Methods, What is the simplified expression for the expression below

To simplify the expression, we will use the following algebraic rules:

• Combining like terms:Terms with the same variable and exponent can be combined.
• Distributing the negative sign:When a negative sign is distributed over a term, it changes the sign of every term within that term.

Step-by-Step Simplification

1. Combine like terms:3x
   • 5x =
   • 2x
2. Distribute the negative sign:2y
   • 7y =
   • 5y
3. Combine the simplified terms:
   • 2x
   • 5y

Illustrative Examples

Original Expression	Simplified Expression
3x + 2y 5x + 7y	-2x 5y

• Intermediate Step 1: 3x – 5x = -2x
• Intermediate Step 2: 2y – 7y = -5y

Query Resolution: What Is The Simplified Expression For The Expression Below

What are the basic steps for simplifying an expression?

1. Identify the mathematical operations involved (addition, subtraction, multiplication, division). 2. Apply algebraic rules (distributive property, combining like terms, factoring) to simplify the expression. 3. Perform the operations in the correct order of precedence.

How can I check if my simplified expression is correct?

Substitute the simplified expression back into the original expression. If the result is the same, your simplification is correct.