Let's carefully analyze the expression:
[tex]\[
12x^3 - 18xy + 24
\][/tex]
Step-by-Step Breakdown:
1. Identify the Terms:
- The expression consists of three terms: [tex]\(12x^3\)[/tex], [tex]\(-18xy\)[/tex], and [tex]\(24\)[/tex].
2. Examine Each Term Separately:
- The term [tex]\(12x^3\)[/tex] is a polynomial term where [tex]\(x\)[/tex] is raised to the third power and then multiplied by 12.
- The term [tex]\(-18xy\)[/tex] involves a multiplication of two variables, [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and then multiplied by [tex]\(-18\)[/tex].
- The term [tex]\(24\)[/tex] is a constant term, which does not involve any variables.
3. Simplification Check:
- Look for common factors or simplifications in each term. Here, each term is already in its simplest form. There are no common variables or like terms that can be further simplified.
4. Expression in Simplified Form:
- After reviewing the expression, we find that it is already in its simplest governed form when expanded.
Summarizing the Expression:
The expression [tex]\(12x^3 - 18xy + 24\)[/tex] is fully simplified and does not need any further steps for simplification. Thus, the final form of the expression remains:
[tex]\[
12x^3 - 18xy + 24
\][/tex]
This is the detailed breakdown of the given mathematical expression.
