Understanding the Expansion of 4(3x) - 2

When dealing with algebraic expressions, it's essential to understand how to expand expressions involving multiplication. Here, we will walk through the process of expanding the expression 4(3x) - 2.

The Distributive Property

The distributive property is a fundamental principle in algebra that allows us to distribute a number across terms inside a parenthesis. It can be expressed as a(b c) ab ac. In the given expression 4(3x) - 2, we will apply the distributive property to expand the multiplication.

Step-by-Step Solution

Let's break down the expression 4(3x) - 2

Distribute the 4: Multiply 4 with 3x and -2 separately. Multiplication: 4 multiplied by 3x is 12x, and 4 multiplied by -2 is -8. Combine the terms: The expression now becomes 12x - 8.

Using the Distributive Property

Let's apply the distributive property to the expression more formally:

Formal Application

The distributive property can be written as a(b) a(c). For our expression, this becomes:

4(3x) - 2

Step 1: Distribute the 4

4 3x - 4 2

Step 2: Perform the multiplications

12x - 8

Algebraic Expansion and its Importance

Understanding how to expand algebraic expressions is crucial for solving more complex equations and understanding the underlying principles of algebra. This skill helps in simplifying expressions, solving equations, and even in more advanced mathematical topics such as calculus.

Related Concepts

Expanding algebraic expressions is closely related to several other key concepts in algebra:

Distributive Property: The principle of distributing a multiplier across a sum or difference. Simplifying Expressions: Reducing an expression to its simplest form. Solving Equations: Finding the value of variables that satisfy the equation.

Conclusion

In conclusion, the expression 4(3x) - 2 expands to 12x - 8 by applying the distributive property.

To expand such expressions:

Distribute the number outside the parentheses to each term inside. Perform the multiplication for each term. Combine like terms, if any.

Always remember to maintain the correct order of operations and keep your work organized for clarity and accuracy.

Frequent Questions

Can you expand 2(4x) 3? What is the distributive property used for? Can the distributive property be applied to more than two terms?

For more detailed explanations and practice, visit the Math is Fun website.

By mastering these techniques, you'll be better equipped to solve a wide range of algebraic problems.