https://file.aiquickdraw.com/mathbot/file/1726152163812vnntdtbg.jpg

The given expression to factor is:

\[
-7x^5y^3z^3 + 28x^2z^2
\]

### Step 1: Identify the Greatest Common Factor (GCF)
First, find the greatest common factor of the two terms:
- For the numerical coefficients: GCF of \(-7\) and \(28\) is \(7\).
- For the variable \(x\): The lowest power of \(x\) is \(x^2\).
- For the variable \(z\): The lowest power of \(z\) is \(z^2\).

Thus, the GCF of the entire expression is \(7x^2z^2\).

### Step 2: Factor out the GCF
Now factor out \(7x^2z^2\) from the expression:

\[
-7x^5y^3z^3 + 28x^2z^2 = 7x^2z^2(-x^3y^3z + 4)
\]

### Final Factored Form:
The completely factored expression is:

\[
7x^2z^2(-x^3y^3z + 4)
\]

Would you like more details or have any further questions?

Here are five related questions for further practice:
1. How do you factor a polynomial with more than two terms?
2. What is the difference between factoring and simplifying an expression?
3. How can you verify that a factored expression is correct?
4. How do you factor an expression when the GCF includes variables with negative exponents?
5. How do you factor an expression when dealing with fractional exponents?

**Tip:** Always double-check your GCF by dividing each term of the polynomial to avoid errors in factoring.

Factor completely: -7x^5y^3z^3 + 28x^2z^2

Learn how to factor the expression -7x^5y^3z^3 + 28x^2z^2 by identifying the Greatest Common Factor (GCF). This problem involves algebraic techniques suitable for Grades 9-12, providing a step-by-step breakdown of factoring using common factors in coefficients and 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