factor using GCF with solution 12x⁴y³-4x⁴y²

To factor the expression \( 12x^4y^3 - 4x^4y^2 \) using the Greatest Common Factor (GCF), follow these steps:

### Step 1: Identify the GCF of the coefficients
- The coefficients are 12 and 4.
- The GCF of 12 and 4 is 4.

### Step 2: Identify the GCF of the variables
- For \(x^4\), both terms have \(x^4\), so the GCF for the \(x\) variable is \(x^4\).
- For the \(y\) terms, \(y^3\) and \(y^2\), the GCF is \(y^2\) (the lowest power of \(y\) present in both terms).

### Step 3: Combine the GCFs
- The overall GCF is \( 4x^4y^2 \).

### Step 4: Factor the GCF out of the expression
- Divide each term by the GCF \(4x^4y^2\):
  \[
  \frac{12x^4y^3}{4x^4y^2} = 3y
  \]
  \[
  \frac{4x^4y^2}{4x^4y^2} = 1
  \]
- The expression inside the parentheses after factoring out the GCF is \(3y - 1\).

### Final Factored Form:
\[
12x^4y^3 - 4x^4y^2 = 4x^4y^2(3y - 1)
\]

### Summary
The expression \(12x^4y^3 - 4x^4y^2\) factors to \(4x^4y^2(3y - 1)\).

Would you like more details on any of the steps or have any questions?

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Here are 8 related questions you might find useful:
1. How do you factor trinomials using the GCF?
2. What is the next step after factoring using the GCF?
3. How do you factor expressions with more than two terms?
4. What happens if there is no common factor between the terms?
5. Can you factor a polynomial completely if the GCF is 1?
6. How do you find the GCF of variables with different exponents?
7. How do you factor out negative common factors?
8. What are the applications of factoring in solving equations?

**Tip:** Always check for a common factor in all terms before attempting more complex factoring methods.

Learn how to factor the expression 12x^4y^3 - 4x^4y^2 using the Greatest Common Factor (GCF) method with a detailed step-by-step solution. Understand the concept of GCF, polynomial factoring, and variable exponents. Suitable for Grades 7-9.

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