Certainly! Let's break down the given expression and see how it can be simplified or understood step-by-step.
We start with the expression:
[tex]\[ x^2 - 6x \][/tex]
### Step 1: Identify the terms
The expression [tex]\( x^2 - 6x \)[/tex] consists of two different terms:
1. [tex]\( x^2 \)[/tex] - This is a quadratic term (a term with [tex]\( x \)[/tex] raised to the power of 2).
2. [tex]\( -6x \)[/tex] - This is a linear term (a term with [tex]\( x \)[/tex] raised to the power of 1).
### Step 2: Examine for like terms
To simplify or rewrite the expression, we look for like terms. Like terms are terms that have the same variable raised to the same power. In this case, [tex]\( x^2 \)[/tex] and [tex]\( -6x \)[/tex] are not like terms because they have different powers of [tex]\( x \)[/tex].
### Step 3: Factoring (Optional)
Sometimes, we look to factor expressions, especially quadratic ones, but in this case, the expression is already in a simplified form. However, if needed, we can factor out the common factor from both terms:
The common factor in both [tex]\( x^2 \)[/tex] and [tex]\( -6x \)[/tex] is [tex]\( x \)[/tex]. So we can factor [tex]\( x \)[/tex] out:
[tex]\[ x(x - 6) \][/tex]
This shows another form of the expression but doesn't change its overall simplified version initially given.
### Step 4: Verify the expression
Since we are not solving an equation but merely simplifying or expanding, our original expression remains:
[tex]\[ x^2 - 6x \][/tex]
### Conclusion
The simplest and most expanded form of the given expression is:
[tex]\[ x^2 - 6x \][/tex]
This confirms that the expression is already in its simplified form.
