91Ó°ÊÓ

Simplifying expressions might seem challenging, but it's all about following a few straightforward steps. When you see an algebraic expression, it typically includes numbers, variables, and sometimes operations such as addition, subtraction, multiplication, or division. The goal of simplifying an expression is to make it as simple as possible.
Look at each part of the expression and see if there are any operations you can perform. For example, when simplifying the expression \(-6m^{3}(3n^{2})\), identify both the constants and the variables:
\[ -6 m^{3} \times 3 n^{2} \]

Here, \-6\ and \3\ are constants, while \m^{3}\ and \^{2}\ are variables. Always handle constants and variables separately.
Remember, simplifying is all about making the expression cleaner and more understandable.

When simplifying algebraic expressions, one of the key steps involves multiplying the constants or numbers. Constants are the numerical values in the expression without variables attached. In our example, we have \-6\ and \3\.
First, multiply these constants together:
\[ -6 \times 3 = -18 \]
By doing this, you simplify the operations involving numbers. Now our expression is reduced to:
\[ -18 m^{3} n^{2} \]
Why is this important? It makes the expression easier to work with in further calculations or when you need to combine it with other terms. Just remember, multiplying constants is straightforward, and dealing with positive and negative signs correctly is crucial.
For instance, a negative multiplied by a positive results in a negative.

Next, let's focus on combining the variables. In the expression, we have \m^{3}\ and \^{2}\. When simplifying terms involving variables:

• Group like terms together.
• If they're the same variable raised to different powers, combine them using the rules of exponents.

However, in our example, the variables are \m\ and \, which are different.
Because they aren't like terms, we cannot combine these variables further. So, we leave them as they are:
\[ -18m^{3}n^{2} \]
When working with different variables, each remains distinct unless you are asked to perform additional operations that might affect them.

This is a key concept in algebra – knowing when variables can be combined and when they should remain separate helps in simplifying expressions correctly.