Simplifying expressions with parentheses is a fundamental skill in algebra that helps you solve equations and understand mathematical relationships better. Let’s break down the process step by step.
- Understand the Order of Operations
Before diving into simplification, it’s crucial to recall the order of operations, often remembered by the acronym PEMDAS:- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
- Distribute and Combine Like Terms
When you see parentheses, your first task is to distribute any numbers or variables outside the parentheses to the terms inside. For example, in the expression $3(2x + 4)$, you distribute the 3 to both $2x$ and 4:$3(2x + 4) = 3 times 2x + 3 times 4 = 6x + 12$
- Simplify Inside the Parentheses
If there are multiple operations inside the parentheses, handle those first. For instance, in the expression $(5 + 3) times 2$, you first simplify inside the parentheses:$(5 + 3) times 2 = 8 times 2 = 16$
- Combine Like Terms
Once the parentheses are simplified or removed, combine like terms to simplify the expression further. Like terms are terms that have the same variables raised to the same power. For example:$4x + 2x = 6x$
Example Problems
Example 1: Simplify $2(3x + 5) + 4(x – 2)$
- Distribute $2$ and $4$:
$2 times 3x + 2 times 5 + 4 times x + 4 times (-2)$
$= 6x + 10 + 4x – 8$
- Combine like terms:
$6x + 4x + 10 – 8 = 10x + 2$
Example 2: Simplify $(2x + 3)(x – 1)$
- Use the distributive property (FOIL method):
$(2x + 3)(x – 1) = 2x times x + 2x times (-1) + 3 times x + 3 times (-1)$
$= 2x^2 – 2x + 3x – 3$
- Combine like terms:
$2x^2 + x – 3$
Conclusion
Simplifying expressions with parentheses involves understanding the order of operations, distributing terms, and combining like terms. Mastering these steps will make solving more complex algebraic equations much easier. Remember, practice is key to getting comfortable with these techniques!