Expand And Simplify X 4 X 5

Expanding and Simplifying x * 4 * 5: A Step-by-Step Guide

This article will guide you through the process of expanding and simplifying the algebraic expression x * 4 * 5. Understanding how to manipulate such expressions is fundamental in algebra and forms the basis for more complex calculations. We'll break down the steps involved, ensuring a clear understanding for both beginners and those looking for a refresher.

What does x * 4 * 5 mean?

This expression represents a multiplication of three terms: a variable 'x', the number 4, and the number 5. The asterisk (*) symbol denotes multiplication. The goal is to simplify this expression into a more concise form.

Step 1: Commutative Property of Multiplication

The commutative property states that the order of multiplication doesn't affect the result. This means we can rearrange the terms without changing the overall value. We can rewrite the expression as:

4 * 5 * x

Step 2: Perform the Numerical Multiplication

Now, let's multiply the numerical values together:

4 * 5 = 20

Step 3: Simplify the Expression

Substitute the result of the numerical multiplication back into the expression:

20 * x

Step 4: Final Simplified Form

Conventionally, we write the numerical coefficient before the variable. Therefore, the simplified form of the expression x * 4 * 5 is:

20x

Understanding the Concept

This seemingly simple example demonstrates core algebraic principles. Understanding the commutative property and the order of operations is crucial for solving more complex algebraic equations. This process involves combining like terms – in this case, the numerical constants – to simplify the expression and make it easier to work with in further calculations. This simplification is essential for efficiency and clarity in mathematical problem-solving.

Beyond the Basics

While this example focuses on a basic algebraic expression, the same principles apply to more complex scenarios. For instance, consider the expression 3x * 2y * 5. You would follow the same steps: first, multiply the numerical coefficients (3 * 2 * 5 = 30), then combine the variables (xy), resulting in the simplified expression 30xy. The key is to always remember the order of operations (PEMDAS/BODMAS) and utilize the commutative property to your advantage when multiplying.

By understanding these fundamental steps, you'll be well-equipped to tackle more intricate algebraic expressions and build a strong foundation in mathematics. Remember to practice regularly to solidify your understanding and build confidence in your algebraic skills.