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The distributive property is a key tool in algebra that allows us to simplify expressions by eliminating parentheses. It states that a number multiplied by a sum or difference is equal to the sum or difference of products. In formula form, it looks like this: \[ a(b + c) = ab + ac \] When confronted with an expression like \( 4x - 2(3x + 8) \), you can apply the distributive property to simplify it. In this case, multiply \( -2 \) by each term inside the parentheses \( (3x + 8)\). This step converts the expression into \( 4x - 6x - 16 \). Remember, keep track of negative signs, as they change the sign of the terms they multiply. This property is particularly useful in making more complex algebraic expressions easier to manage.

Once you have an expression without parentheses, the next step is often to combine like terms. Like terms are those that have the same variable raised to the same power. In our example, \( 4x - 6x - 16 \), the terms \( 4x \) and \( -6x \) are like terms because they both contain the variable \( x \). Here's a simple way to remember it:

• Look for terms with the same letter and exponent.
• Add or subtract the coefficients (numbers in front of the variable).

So, combining \( 4x \) and \( -6x \) gives us \( -2x \). Don’t forget to bring down any constants, like \(-16\), which must accompany the simplified expression, leaving you with \(-2x - 16\). This step helps tidy up your work into a clearer final expression.

Prealgebra is all about building a foundation for understanding algebra. It involves learning how to manipulate and simplify expressions, which is crucial as you move on to more complex math problems. In exercises like \( 4x - 2(3x + 8) \), you learn several important skills:

• Understanding Variables: Recognize how letters represent numbers.
• Order of Operations: Apply the correct sequence of arithmetic operations.
• Balancing Equations: Use properties like the distributive property to keep equations equal while transforming them.

The goal in prealgebra is to give you tools to approach problems confidently. This exercise demonstrates the importance of strategic thinking in math, allowing you to break down problems and solve them efficiently. These skills are vital stepping stones to understanding more advanced algebraic concepts.