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In algebra, it is essential to understand the difference between constants and variables.

Constants are numbers that have a fixed value, no matter what. For example, in the problem: \(8 x(6)(y)\), the numbers 8 and 6 are constants.

Variables, on the other hand, are symbols that represent changing values. They are often denoted by letters such as x, y, or z. In the expression \(8 x(6)(y)\), both x and y are variables.

Understanding this difference is key because it affects how you manipulate the expression. Knowing which parts of your equation are constants and which are variables will help simplify it correctly.

When simplifying algebraic expressions, knowing how to properly multiply constants and variables is crucial.

Multiplication in algebra works the same as in arithmetic but with an added twist of variables. Let's break it down:

First, multiply the constants. In the problem \(8 x(6)(y)\), you multiply 8 and 6 first:

• 8 times 6 equals 48.

Next, write down the variables next to the new constant. So the expression now looks like this: \(48xy\).

Multiplying variables together follows simple algebraic rules too. For instance, x \( \times \) y just becomes xy. There are no additional numbers to deal with when multiplying variables directly. This makes it easier to simplify the expression step-by-step.

Algebraic manipulation is the process of rearranging and combining terms in an algebraic expression to simplify it.

In our example, \(8 x(6)(y)\), the first step was to rearrange and group the constants and variables together. This allows for straightforward multiplication of constants and makes sure the variables follow.

The rearrangement looked like this: \((8 \cdot 6) x y\).
Once you've grouped everything properly, you can multiply the constants first, as shown before: \(8 \times 6 = 48\).

Now, you have \(48xy\). The expression \(48xy\) is simplified because:

• All constants are combined into one number.
• The variables are neatly arranged.

By following these steps, you can make even complex algebraic expressions easier to handle and solve. Mastering algebraic manipulation is about practice and understanding each step thoroughly.