Let’s break down the given expression step-by-step:
[tex]\[ 5xy - 5y - 3x - 9 \][/tex]
We want to confirm the form and structure of this expression and interpret its components. Here's how the expression is structured:
1. Identify the terms:
The expression consists of four terms:
- [tex]\(5xy\)[/tex]
- [tex]\(-5y\)[/tex]
- [tex]\(-3x\)[/tex]
- [tex]\(-9\)[/tex]
2. Combine like terms:
Since the given expression already has like terms grouped together (there are no additional like terms to combine), it remains as it is:
[tex]\[ 5xy - 5y - 3x - 9 \][/tex]
3. Interpret the expression:
To gain a better understanding, let’s outline what each term represents:
- [tex]\(5xy\)[/tex] indicates a term that is a product of both [tex]\(x\)[/tex] and [tex]\(y\)[/tex], scaled by 5.
- [tex]\(-5y\)[/tex] indicates a term that involves [tex]\(y\)[/tex] scaled by [tex]\(-5\)[/tex].
- [tex]\(-3x\)[/tex] indicates a term that involves [tex]\(x\)[/tex] scaled by [tex]\(-3\)[/tex].
- [tex]\(-9\)[/tex] is a constant term.
Thus, the given algebraic expression:
[tex]\[ 5xy - 5y - 3x - 9 \][/tex]
is correctly structured with four terms contributing to the overall expression.
In summary, the expression cannot be simplified further by combining terms, and no additional factoring or reduction can be applied based purely on distributing multiplication or combining like terms. This makes [tex]\( 5xy - 5y - 3x - 9 \)[/tex] the most refined and accurate form of the given expression.
