Simplifying Algebraic Expressions: A Step-by-Step Guide
Learning to simplify algebraic expressions is a fundamental skill in mathematics. This guide will walk you through the process of simplifying the given expression 2a3b^2 - 4^2 with detailed steps and explanations. By understanding these methods, you can efficiently solve similar algebraic expressions.
How to Simplify the Expression 2a3b^2 - 4^2
The expression 2a3b^2 - 4^2 involves both multiplication and exponentiation. Let's break down this expression step-by-step to see how it simplifies.
Step 1: Understand the Expression Components
2a3b^2: This term contains multiple variables and an exponent. Specifically, it represents the multiplication of 2, the variable a, the variable b squared, and the multiplier 3. 4^2: This is a simple exponentiation, where 4 is raised to the power of 2.Step 2: Rewrite the Expression Clearly
The expression can be rewritten to ensure clarity:
2a3b^2 - 4^2
Step 3: Apply the Distributive Property
First, we need to clarify the expression. The term 2a3b^2 can be written as:
2a(3b^2) 2a3b^2
The correct form is:
2a3b^2 is written as 2a3b^2.
Step 4: Simplify the Expression
Now, let's simplify the expression according to the steps provided:
First, rewrite the expression clearly:
2a3b^2 - 4^2
Apply the distributive property:
2a(3b^2) - 4^2 2a3b^2 - 4^2
Simplify the expression:
2a3b^2 - 4^2 2a^2 3b^2 - 4^2
4a^2 9b^2 - 12ab - 16
Here, the expression is simplified to:
4a^2 9b^2 - 12ab - 16
Final Simplified Expression
The final simplified expression is:
4a^2 9b^2 - 12ab - 16
Understanding the Components of the Expression
ab^2
Let's break down the term ab^2 further:
ab^2 a^2b^2 2ab
The term 2ab^2 can be written as:
2a3b^2 4a^2 9b^2 - 12ab - 16
Final Expression
The final expression, after all the simplifications, becomes:
4a^2 9b^2 - 12ab - 16
Conclusion
In conclusion, simplifying algebraic expressions requires a clear understanding of the components and the application of the correct mathematical rules. By following the steps outlined in this guide, you can simplify complex algebraic expressions efficiently and accurately.