28x^(4)y^(2) + 14x^(3)y^(2) − 7x^(2)y^(2)
Common monomial factor
Remaining factor 
Factored form

To factor the given expression \(28x^4y^2 + 14x^3y^2 - 7x^2y^2\), we'll start by finding the **common monomial factor**.

### Step 1: Identify the Common Monomial Factor
- **Coefficients**: The coefficients are 28, 14, and -7. The greatest common factor (GCF) of these numbers is 7.
- **Variables**: The expression contains \(x^4\), \(x^3\), and \(x^2\). The lowest power of \(x\) is \(x^2\).
- **More Variables**: The expression also contains \(y^2\), \(y^2\), and \(y^2\). The lowest power of \(y\) is \(y^2\).

So, the **common monomial factor** is **\(7x^2y^2\)**.

### Step 2: Factor Out the Common Monomial Factor
Now, divide each term by the common factor \(7x^2y^2\):

\[
28x^4y^2 \div 7x^2y^2 = 4x^2
\]
\[
14x^3y^2 \div 7x^2y^2 = 2x
\]
\[
-7x^2y^2 \div 7x^2y^2 = -1
\]

### Step 3: Write the Remaining Factor
The remaining factor after factoring out \(7x^2y^2\) is \(4x^2 + 2x - 1\).

### Step 4: Write the Factored Form
The fully factored form of the expression is:

\[
7x^2y^2(4x^2 + 2x - 1)
\]

---

**Summary:**
- **Common Monomial Factor**: \(7x^2y^2\)
- **Remaining Factor**: \(4x^2 + 2x - 1\)
- **Factored Form**: \(7x^2y^2(4x^2 + 2x - 1)\)

Would you like more details or have any questions?

### Related Questions:
1. How can you factor the remaining quadratic \(4x^2 + 2x - 1\)?
2. What is the process to find the GCF of polynomials?
3. How do you apply the distributive property to expand a factored expression?
4. What are the different methods to factor quadratic polynomials?
5. How does factoring help in solving polynomial equations?

### Tip:
When factoring polynomials, always start by identifying and factoring out the greatest common monomial factor to simplify the expression.

Learn how to factor the polynomial 28x^4y^2 + 14x^3y^2 - 7x^2y^2 step-by-step with detailed explanations. This problem covers key algebraic concepts, including polynomial factoring. Suitable for high school students and above.

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