How to Simplify the Expression 4a - b[2a - 38a - 5c3]
Understanding and simplifying algebraic expressions, such as 4a - b[2a - 38a - 5c3], can be a daunting task, especially for those without a strong grasp on the order of operations. In this guide, we'll walk through the process step-by-step, ensuring that you can confidently handle similar expressions.
The Order of Operations: PEMDAS or PERMDAS?
The order of operations is a fundamental principle in algebra that ensures expressions are evaluated consistently. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) is commonly used. However, for a more comprehensive system, you might consider PERMDAS (Parentheses, Exponents, Roots, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Step-by-Step Simplification of 4a - b[2a - 38a - 5c3]
Our goal is to simplify the expression 4a - b[2a - 38a - 5c3]. Let's break it down step-by-step.
Step 1: Distribute the -3 Inside the Brackets
Start by simplifying the expression inside the brackets: 2a - 38a - 5c3.
To do this, distribute the -3 to the terms within the brackets:
38a - 5c3 24a - 15c
This simplifies to:
2a - 24a - 15c3 2a - 24a - 15c
Step 2: Combine Like Terms Inside the Brackets
Next, combine the like terms within the brackets:
2a - 24a -22a
The expression inside the brackets now becomes:
-22a - 15c3 -22a - 15c
Step 3: Substitute Back into the Original Expression
Now, substitute this simplified result back into the original expression:
4a - b[-22a - 15c]
Step 4: Distribute the -b
Next, distribute the -b across the terms inside the brackets:
4a - b(-22a - 15c)
4a 22ab - 15bc - 3b
The expression is now simplified to:
22ab 4a - 15bc - 3b
Final Expression
The simplified form of the expression 4a - b[2a - 38a - 5c3] is:
22ab 4a - 15bc - 3b
Why PERMDAS is Superior to PEMDAS
Some educators, like the author, prefer PERMDAS (Parentheses, Exponents, Roots, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). This system includes roots, which are often overlooked in PEMDAS. Using PERMDAS encourages a more comprehensive understanding of the order of operations, making it easier to handle complex expressions.
By following the steps outlined in this guide, you can confidently simplify similar expressions. The key is to start with the innermost brackets and work your way outwards, distributing coefficients and combining like terms as necessary. With practice, this process will become second nature, and you'll be able to handle even more complex algebraic expressions with ease.