To factor the expression \( 9x^4yz^2 + 33z^4 \), let's break it down step by step.

### Expression:
\[
9x^4yz^2 + 33z^4
\]

### Step 1: Find the common factors

1. **Numerical coefficients**: The greatest common factor (GCF) of 9 and 33 is 3 (since 9 = \( 3 \times 3 \) and 33 = \( 3 \times 11 \)).
   
2. **Variable \( z \)**: The lowest power of \( z \) is \( z^2 \) (since the terms have \( z^2 \) and \( z^4 \)).
   
3. **Variables \( x \) and \( y \)**: These do not appear in both terms, so they cannot be factored out.

### Step 2: Factor out the common terms

The common factor between the two terms is \( 3z^2 \).

\[
3z^2(3x^4y + 11z^2)
\]

### Final factored expression:

\[
3z^2(3x^4y + 11z^2)
\]

Let me know if you need further clarification or more details.

### Relative Questions:
1. How do you determine the greatest common factor between terms?
2. What is the best way to factor polynomials involving powers of variables?
3. How do you factor expressions with multiple variables?
4. What happens if the terms don't have a common factor?
5. Can factoring help in simplifying or solving equations?

**Tip**: Always start by factoring out the greatest common factor before looking for other factoring techniques.

Learn how to factor the polynomial expression 9x^4yz^2 + 33z^4 with a step-by-step solution. This problem covers polynomial factoring techniques and is suitable for advanced high school students. Explore more about factoring polynomials involving multiple variables.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation