Solving Algebraic Expressions: A Comprehensive Guide

In the world of mathematics, understanding how to solve algebraic expressions is a key skill that every student must master. This article provides a detailed breakdown of the process, specifically focusing on the given expression: 8xy - [7x - {5x - 4x - 3x - y - 2y}]. By the end of this guide, you will have a clear understanding of the steps involved and be able to tackle similar algebraic expressions with confidence.

Step-by-Step Solution

Let's begin by breaking down the given algebraic expression: 8xy - [7x - {5x - 4x - 3x - y - 2y}]

Step 1: Begin by simplifying the innermost brackets. Notice that {5x - 4x - 3x - y - 2y} can be simplified to {5x - 4x - 3x - y - 2y} Step 2: Combine like terms in the innermost brackets. 5x - 4x - 3x x -y - 2y -3y Therefore, {5x - 4x - 3x - y - 2y} simplifies to {x - 3y} Step 3: Substitute the simplified result back into the original expression. The expression now becomes 8xy - [7x - (x - 3y)] Step 4: Simplify the expression inside the brackets. 7x - (x - 3y) 7x - x 3y 7x - x 3y 6x 3y Step 5: Substitute the simplified result back into the expression. The expression now becomes 8xy - (6x 3y) Step 6: Distribute the negative sign across the terms in the parentheses. 8xy - 6x - 3y Step 7: Combine like terms in the expression. In this case, there are no like terms to combine. The final simplified expression is: 5x

Understanding the Process of Algebraic Expression Solving

Solving algebraic expressions involves a series of logical steps that help you break down complex expressions into simpler, more manageable components. Here are the key steps:

Step 1: Identify and Simplify Inside Brackets Step 2: Use the Distributive Property to Remove Brackets Step 3: Combine Like Terms

Identify and Simplify Inside Brackets - This is the first step in solving any algebraic expression. You need to look for any operations that can be simplified inside brackets, such as combining like terms.

Use the Distributive Property to Remove Brackets - Once you have simplified inside the brackets, use the distributive property to remove the brackets. This involves distributing any coefficients or variables outside the brackets to the terms inside.

Combine Like Terms - After removing the brackets, combine the like terms to simplify the expression further. This step is crucial in ensuring that the expression is fully simplified.

Key Points to Remember in Algebraic Problem-Solving

Here are some key points to keep in mind when solving algebraic expressions:

Always start by identifying and simplifying the innermost brackets. Use the distributive property to ensure that all terms are correctly propagated. Combine like terms to further simplify the expression. Double-check your work for any arithmetic or algebraic errors.

By following these steps and key points, you can confidently solve a wide range of algebraic expressions, such as the one we discussed: 8xy - [7x - {5x - 4x - 3x - y - 2y}].

Conclusion

Mastering the art of solving algebraic expressions is a fundamental skill in mathematics. By following the step-by-step process outlined in this guide, you can simplify even the most complex expressions. Remember to always break down the problem, simplify step-by-step, and check your work.

Whether you are a student preparing for exams or a professional needing to apply algebra in your work, understanding algebraic expressions is a valuable skill. With practice and a solid grasp of the key concepts, you will be well on your way to becoming an algebraic problem-solving expert.

Additional Resources

For further practice and detailed guidance on algebraic expressions, consider exploring the following resources:

Mathway - Algebraic Expression Solver Khan Academy - Algebra Lessons Math Is Fun - Algebra Section