The expression you provided is:

\[
\frac{10a^2 + 72ab}{63}
\]

### Step 1: Simplify the numerator
First, let's factor out the greatest common factor (GCF) from the numerator. The terms are \(10a^2\) and \(72ab\), and the GCF between 10 and 72 is 2. Also, both terms contain the variable \(a\), so we can factor out \(2a\).

\[
10a^2 + 72ab = 2a(5a + 36b)
\]

### Step 2: Simplify the fraction
Now substitute the factored form of the numerator back into the original expression:

\[
\frac{2a(5a + 36b)}{63}
\]

At this point, there are no common factors between 2 and 63, so the fraction is already in its simplest form. Therefore, the simplified expression is:

\[
\frac{2a(5a + 36b)}{63}
\]

Would you like more details on any of the steps? 

Here are 5 related questions to deepen understanding:
1. How do you find the greatest common factor (GCF) between two terms?
2. Can this expression be further simplified if additional variables are known?
3. How would this process change if the denominator had variables?
4. What happens if you try to factor the denominator?
5. How does factoring help in solving algebraic expressions?

**Tip:** Always check for common factors in both the numerator and the denominator to simplify the fraction fully!

This solution demonstrates how to simplify the algebraic expression (10a^2 + 72ab) / 63 by factoring the numerator and reducing the fraction. Learn how to apply factoring techniques, such as finding the greatest common factor (GCF), and understand key algebraic concepts. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation