Certainly! Let's go through the detailed step-by-step process to simplify the given expression: [tex]\(8a^6 - 4bx^4 + 2cx^2\)[/tex].
### Step 1: Identify Each Term
The given expression consists of three terms:
1. [tex]\(8a^6\)[/tex]
2. [tex]\(-4bx^4\)[/tex]
3. [tex]\(2cx^2\)[/tex]
### Step 2: Understand the Expression Structure
This expression is a polynomial with terms involving different powers of [tex]\(a\)[/tex] and [tex]\(x\)[/tex]. Specifically:
- The term [tex]\(8a^6\)[/tex] involves the variable [tex]\(a\)[/tex].
- The term [tex]\(-4bx^4\)[/tex] involves variables [tex]\(b\)[/tex] and [tex]\(x\)[/tex].
- The term [tex]\(2cx^2\)[/tex] involves variables [tex]\(c\)[/tex] and [tex]\(x\)[/tex].
### Step 3: Combine Like Terms (if any)
In this specific polynomial, no like terms can be combined as each term has different powers of [tex]\(x\)[/tex] and involves different combinations of the variables [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
### Step 4: Factor If Possible (not applicable here)
Each term is already in its simplest form, and there are no common factors to factor out within this polynomial expression.
### Step 5: Verify and Simplify
Upon verification, the expression [tex]\( 8a^6 - 4bx^4 + 2cx^2 \)[/tex] is found to be in its simplest form already.
### Conclusion
The expression [tex]\(8a^6 - 4bx^4 + 2cx^2\)[/tex] is fully simplified and represents a polynomial with three terms involving different variables and powers. Each term is distinct and cannot be further simplified or combined with the others.
So, the simplified form of the expression is:
[tex]\[
8a^6 - 4bx^4 + 2cx^2
\][/tex]
This polynomial is precisely structured as given and represents the combination of terms with their respective coefficients and variables clearly defined.
