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Understanding the distributive property is essential for simplifying algebraic expressions. It allows you to multiply a single term by each term inside a parenthesis. For instance, when you see an expression like \(3(a - b)\), you distribute the 3 to both \(a\) and \(-b\), resulting in \(3a - 3b\). The distributive property works the same way with subtraction, such as with \(-2(a + b)\), which becomes \(-2a - 2b\). It's like handing out apples from a basket to a line of people; each person gets the same number of apples (the multiplier) multiplied by the quantity they already have (the terms inside the parentheses).

Remember to consider the signs in front of the parentheses, as they are part of the number you are distributing. This property is the first step in our exercise, transforming the initial expression into one that can be worked on further.

Once the distributive property has been applied, the next step is to look for like terms. Like terms are terms that have the exact same variable raised to the same power. For example, \(3a\) and \(-2a\) are like terms because they both contain the variable \(a\). Similarly, \(-3b\) and \(-2b\) are like terms because they both contain the variable \(b\).

To combine like terms, simply add or subtract their coefficients (the numbers in front of the variables). In our exercise, we combine \(3a\) with \(-2a\) to get \(a\), and we combine \(-3b\) with \(-2b\) to get \(-5b\). Imagine you're organizing fruit by type; you group apples with apples and bananas with bananas to see how many of each you have in total. This simplifies the expression and brings you one step closer to solving the problem.

Algebraic subtraction involves the removal of one algebraic expression from another. This can often require rearranging the expression to make like terms adjacent to each other, facilitating their combination. When you subtract the coefficients of the like terms, you are performing algebraic subtraction. In the given exercise, once we combine like terms, we subtract the coefficients of \(a\) and \(b\) to find our simplified expression, \(a - 5b\).

It's important to pay attention to the signs. Subtracting a negative is the same as adding a positive. So if you have \(-3b - (-2b)\), you're essentially doing \(-3b + 2b\), which simplifies to \(-b\). This is a crucial final step in simplifying algebraic expressions and ensuring that your work is accurate.