Expanding Expressions: A Guide to Simplifying 2(3a - 2b)
In algebra, expanding expressions is a fundamental skill that helps in simplifying and solving equations. One of the most common operations used in algebra is the distributive property. This property states that multiplying a number by a sum is the same as multiplying each addend in the sum by the number separately and then adding the products.
Understanding the Distributive Property
The distributive property is represented as:
a(b c) ab ac
In the given expression, 2(3a - 2b), the number outside the parentheses is 2. To expand this expression, we apply the distributive property by multiplying 2 with each term inside the parentheses.
Step-by-Step Solution
Method 1:
Identify the number outside the parentheses: 2. Multiply this number by the first term inside the parentheses: 2 × 3a 6a. Multiply the same number by the second term inside the parentheses: 2 × -2b -4b. Add the resulting terms: 6a - 4b.Thus, we have the expanded form:
Method 2: Alternative Approach
Recognize that multiplying a binomial by a monomial can be approached by distributing. Apply the distributive property directly: 2(3a - 2b) 2 × 3a - 2 × 2b. Calculate the multiplication: 2 × 3a 6a and 2 × -2b -4b. Combine the terms: 6a - 4b.Explanation of the Steps
Step 1: Identify the number outside the parentheses. In this case, it is 2.
Step 2: Multiply this number by the first term inside the parentheses (3a). The multiplication of 2 and 3a gives 6a.
Step 3: Multiply the same number (2) by the second term inside the parentheses (-2b). The multiplication of 2 and -2b gives -4b.
Step 4: Summarize the results of the multiplication to get the final expanded form, which is 6a - 4b.
Conclusion
Understanding and applying the distributive property is essential in algebra. It is not only a fundamental concept but also a powerful tool for simplifying and solving more complex equations. By mastering the process of expanding expressions, students and learners can tackle a wide range of algebraic problems with confidence.