10a - 25 + 5b

2 min read 26-02-2025

Simplifying Algebraic Expressions: A Deep Dive into 10a - 25 + 5b

This article explores the simplification of the algebraic expression 10a - 25 + 5b. We'll break down the process step-by-step, covering fundamental algebraic concepts and demonstrating how to arrive at the most simplified form. Understanding this process is crucial for anyone studying algebra, as it forms the basis for more complex mathematical operations.

Understanding the Components

Before we begin simplifying, let's identify the components of our expression: 10a - 25 + 5b.

10a: This is a term representing the product of 10 and the variable 'a'. The '10' is the coefficient, and 'a' is the variable.
-25: This is a constant term, a numerical value without a variable.
5b: This is another term, representing the product of 5 and the variable 'b'. '5' is the coefficient, and 'b' is the variable.

These three terms are combined through addition and subtraction.

The Concept of Like Terms

The key to simplifying algebraic expressions lies in identifying "like terms." Like terms are terms that contain the same variables raised to the same power. In our expression, 10a and 5b are not like terms because they have different variables (a and b). -25 is a constant term and therefore isn't like either of the variable terms.

Simplifying the Expression

Since there are no like terms in the expression 10a - 25 + 5b, we cannot combine them further. The expression is already in its simplest form. We can rearrange the terms for aesthetic reasons, but the mathematical value remains the same. A common convention is to arrange terms alphabetically:

5b + 10a - 25

This is the simplified version of the original expression.

Further Exploration: What if there were like terms?

Let's consider a slightly different expression to illustrate what happens when like terms are present:

10a + 5a - 25 + 5b

In this case, 10a and 5a are like terms. We can combine them by adding their coefficients:

10a + 5a = 15a

The simplified expression would then be:

15a + 5b - 25

Applying the Concepts: Practice Problems

Here are a few practice problems to test your understanding:

Simplify: 7x + 3y - 2x + 8y
Simplify: 4m - 6n + 12 + 2n - 3m - 5
Simplify: 2(3p + 4q) - 5p + q

Remember, the key to simplifying algebraic expressions is identifying like terms and combining them using addition or subtraction. Once you've mastered this fundamental skill, you'll be well-prepared to tackle more advanced algebraic concepts. If you have any questions, please leave a comment below!