Alright, let's break down the expression [tex]\(4x^3 - 3z^2\)[/tex] step by step.
### Step 1: Understanding the Terms
Firstly, the expression is made up of two terms: [tex]\(4x^3\)[/tex] and [tex]\(-3z^2\)[/tex].
- [tex]\(4x^3\)[/tex]: This term represents 4 times the cube of [tex]\(x\)[/tex].
- [tex]\(-3z^2\)[/tex]: This term represents -3 times the square of [tex]\(z\)[/tex].
### Step 2: Analyzing the Expression Structure
Let's analyze what each part of the expression means:
- The coefficient of [tex]\(x^3\)[/tex] is 4. This means if [tex]\(x\)[/tex] is some number [tex]\(a\)[/tex], then [tex]\(4x^3\)[/tex] will be [tex]\(4a^3\)[/tex].
- The coefficient of [tex]\(z^2\)[/tex] is -3. This means if [tex]\(z\)[/tex] is some number [tex]\(b\)[/tex], then [tex]\(-3z^2\)[/tex] will be [tex]\(-3b^2\)[/tex].
### Step 3: Simplifying and Plugging Values
If you need to evaluate this expression for particular values of [tex]\(x\)[/tex] and [tex]\(z\)[/tex], just substitute those values into the expression and simplify.
For example, if [tex]\(x\)[/tex] = 2 and [tex]\(z\)[/tex] = 1, you would substitute these values in as follows:
1. Compute [tex]\(x^3\)[/tex]:
[tex]\[ (2)^3 = 8 \][/tex]
2. Multiply by 4:
[tex]\[ 4 \times 8 = 32 \][/tex]
3. Compute [tex]\(z^2\)[/tex]:
[tex]\[ (1)^2 = 1 \][/tex]
4. Multiply by -3:
[tex]\[ -3 \times 1 = -3 \][/tex]
5. Combine the results:
[tex]\[ 32 - 3 = 29 \][/tex]
Thus, the expression [tex]\(4x^3 - 3z^2\)[/tex] evaluates to 29 when [tex]\(x = 2\)[/tex] and [tex]\(z = 1\)[/tex].
### Step 4: General Form
However, without specific values of [tex]\(x\)[/tex] and [tex]\(z\)[/tex], the expression [tex]\(4x^3 - 3z^2\)[/tex] represents a combination of operations on the variables [tex]\(x\)[/tex] and [tex]\(z\)[/tex], and this is the simplest form it can be presented in.
To sum up:
- The expression is composed of the terms [tex]\(4x^3\)[/tex] and [tex]\(-3z^2\)[/tex].
- These terms involve raising [tex]\(x\)[/tex] to the third power, multiplying by 4, and raising [tex]\(z\)[/tex] to the second power, multiplying by -3.
- The final result is a combination of these two terms: [tex]\(4x^3 - 3z^2\)[/tex], which cannot be simplified further without specific values for [tex]\(x\)[/tex] and [tex]\(z\)[/tex].
Therefore, the given expression [tex]\(4x^3 - 3z^2\)[/tex] is fully simplified and correctly structured.
