Simplifying Algebraic Expressions: 4x-3(x-2y)+1/2(6x-8y) in Standard Form
In algebra, simplifying expressions is a crucial step in solving equations and manipulating formulas. One way to simplify an expression is to rewrite it in standard form, which makes it easier to compare and operate with other expressions. In this article, we will simplify the expression 4x-3(x-2y)+1/2(6x-8y) into its standard form.
Step 1: Expand the Parentheses
The first step is to expand the parentheses using the distributive property of multiplication over addition. This property states that a(b+c) = ab + ac.
Let's expand the first set of parentheses:
-3(x-2y) = -3x + 6y
The expanded expression becomes:
4x - 3x + 6y + 1/2(6x-8y) + 1
Step 2: Expand the Second Set of Parentheses
Now, let's expand the second set of parentheses:
1/2(6x-8y) = 3x - 4y
The expanded expression becomes:
4x - 3x + 6y + 3x - 4y + 1
Step 3: Combine Like Terms
In this step, we combine the like terms, which are terms with the same variable and coefficient.
Combine the x terms:
4x - 3x + 3x = 4x - 3x + 3x = 4x
Combine the y terms:
6y - 4y = 2y
The simplified expression becomes:
4x + 2y + 1
Standard Form
The expression 4x-3(x-2y)+1/2(6x-8y) has been simplified into its standard form:
4x + 2y + 1
In standard form, the expression is written in a concise and easy-to-read format, making it simpler to work with in algebraic operations.
