91Ó°ÊÓ

To start, let's dive into the distributive property. This fundamental principle in prealgebra helps us handle expressions wrapped in parentheses. The distributive property states that for any numbers or variables, a(b + c) = ab + ac.

For example, if you have 3(x + 4), you need to multiply both x and 4 by 3. Hence, 3(x + 4) = 3x + 12.

This step is crucial for simplifying expressions that include parentheses. In our problem, we first encounter 2(s + 6). When applying the distributive property here, we multiply s and 6 by 2, giving us 2s + 12.

We do the same for the second part of the expression, -(8s - t). Here, we distribute the -1 across the terms inside the parentheses, resulting in -8s + t.

After distributing, the next step involves combining like terms. 'Like terms' are terms that have the same variable raised to the same power. In simpler terms, they look alike!

For example, 3x and -4x are like terms because they both contain the variable x. Similarly, 5t and t are like terms because they both contain the variable t.

Once you've distributed in your expression, collect all like terms. In the exercise, we end up with: 2s + 12 - 8s + t + 6t.

Here, 2s and -8s are like terms, and t and 6t are like terms. Group them together to see what can be simplified further. Remember, like terms can only combine into one another.

The final step is simplifying the expression by combining the like terms. Once you’ve identified the like terms, add or subtract their coefficients (the numerical part) while keeping the variable part the same.

In our expression, we have 2s - 8s + t + 6t + 12.

First, combine the s terms: 2s - 8s = -6s.

Next, combine the t terms: t + 6t = 7t.

Lastly, we have the constant term 12, which doesn’t need to combine with anything else.

Hence, our simplified expression becomes: -6s + 7t + 12.

Remember, simplifying expressions makes them easier to work with and is essential for solving more complex algebraic problems down the line.