Simplifying Algebraic Expressions: A Comprehensive Guide

Understanding and Simplifying 2a - 5^2

Understanding and simplifying algebraic expressions is a fundamental skill in mathematics. This guide will walk you through the process of simplifying the expression 2a - 5^2. We'll cover the necessary steps, including expanding the expression and applying the FOIL method to achieve a simplified form.

Expanding the Equation

To begin, let's expand the given equation: 2a - 5^2.

Expansion: First, consider the term 5^2. Remember that squaring 5 results in 25. Now, the equation becomes 2a - 25.

Multiplying and Applying the FOIL Method

While the equation initially appears to be a simple subtraction, there's an added step if we want to make sure we understand it completely. Let's further illustrate the process by multiplying 2a - 5 by itself (i.e., squaring it). Here's how it's done:

Squaring the Expression:

Multiply 2a by each term in the expression: 2a times; (2a - 5). Multiply -5 by each term in the expression: -5 times; (2a - 5).

Expanding Each Term:

First Term: 2a times; 2a 4a^2 Outer Term: 2a times; -5 -10a Inner Term: -5 times; 2a -10a Last Term: -5 times; -5 25

Simplifying the Result:

Now we combine all these terms:

4a^2 (from the first term) -10a (from the outer and inner terms, which combine to -20a) 25 (from the last term)

Putting it all together, we get:

2a - 5^2 4a^2 - 20a 25

Conclusion and Further Study

By understanding the step-by-step process, you can simplify and manipulate algebraic expressions more effectively. This skill is crucial in various areas of mathematics, such as solving quadratic equations and understanding polynomial expressions.

For further study, consider exploring more complex expressions and applying the FOIL method to other quadratic expressions. Utilizing online resources and practicing problems will help solidify your understanding of these mathematical principles.

Key Takeaways: Understanding and simplifying algebraic expressions is essential for solving more complex mathematical problems. The FOIL method can be applied to simplify squared expressions more completely. Practice and further study are key to mastering algebraic expression manipulation.