To factor the expression \(10a^2 + 20a\) using the Greatest Common Factor (GCF), follow these steps:

### Step 1: Identify the GCF of the coefficients
- The coefficients are 10 and 20.
- The GCF of 10 and 20 is 10.

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

### Step 3: Combine the GCFs
- The overall GCF is \(10a\).

### Step 4: Factor the GCF out of the expression
- Divide each term by the GCF \(10a\):
  \[
  \frac{10a^2}{10a} = a
  \]
  \[
  \frac{20a}{10a} = 2
  \]
- The expression inside the parentheses after factoring out the GCF is \(a + 2\).

### Final Factored Form:
\[
10a^2 + 20a = 10a(a + 2)
\]

### Summary
The expression \(10a^2 + 20a\) factors to \(10a(a + 2)\).

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

---

Here are 8 related questions you might find useful:
1. How do you factor trinomials by finding the GCF?
2. What is the difference between factoring and expanding an expression?
3. How do you handle factoring when one term is negative?
4. Can you factor expressions with more than two terms using the GCF?
5. What are some real-world applications of factoring polynomials?
6. How do you factor a quadratic expression completely?
7. How can you verify that your factorization is correct?
8. What happens if the GCF is 1?

**Tip:** After factoring, you can check your work by expanding the expression to ensure it matches the original expression.

Learn how to factor the expression 10a² + 20a using the Greatest Common Factor (GCF) method. Follow step-by-step instructions and understand the concept of factoring polynomials. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation