To address the mathematical expression [tex]\(343 v^3 + 27 w\)[/tex], let's break it down and analyze it step-by-step.
### Step 1: Understanding the Expression
The given expression is:
[tex]\[343 v^3 + 27 w\][/tex]
Here, we have two variables:
- [tex]\(v\)[/tex]
- [tex]\(w\)[/tex]
### Step 2: Coefficients and Exponents
Let's look at the terms individually:
1. First Term: [tex]\(343 v^3\)[/tex]
- The coefficient is 343.
- The variable is [tex]\(v\)[/tex] raised to the power of 3.
2. Second Term: [tex]\(27 w\)[/tex]
- The coefficient is 27.
- The variable is [tex]\(w\)[/tex], which is implicitly raised to the power of 1 (since any variable without an explicit exponent is understood to be raised to the power of 1).
### Step 3: Representation
Combining these two terms, the entire expression can be written as:
[tex]\[343 v^3 + 27 w\][/tex]
### Summary
The expression [tex]\(343 v^3 + 27 w\)[/tex] is already in its simplest form, consisting of a cubic term and a linear term with respect to two different variables, [tex]\(v\)[/tex] and [tex]\(w\)[/tex]. This expression does not require any further simplification or factorization.
Therefore, the given mathematical expression is:
[tex]\[343 v^3 + 27 w\][/tex]
