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The task asks to factor the given expressions. Let's break it down:

### a. \( 6x + 6 \)
We can factor out the greatest common factor (GCF), which is 6:
\[
6x + 6 = 6(x + 1)
\]
So, the factored form is:
\[
6(x + 1)
\]

### b. \( 5x^2 + 30x \)
Similarly, the GCF here is \( 5x \):
\[
5x^2 + 30x = 5x(x + 6)
\]
So, the factored form is:
\[
5x(x + 6)
\]

Let me know if you'd like more details or have any questions!

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Here are 5 related questions for further practice:
1. How would you factor \( 10x^2 + 20x \)?
2. Can you factor \( 12x^2 - 8x \)?
3. What is the factored form of \( 7x^2 + 14x \)?
4. How would you factor \( 9x^2 - 3x \)?
5. Can you find the common factor of \( 15x^3 + 45x^2 \)?

**Tip**: Always start by finding the greatest common factor (GCF) when factoring any expression!

Factorize the expressions: a. 6x + 6, b. 5x^2 + 30x

Explore the step-by-step process of factoring algebraic expressions, starting with basic examples like 6x + 6 and 5x^2 + 30x. Learn how to identify and factor out the greatest common factor to simplify expressions. Suitable for middle school students learning algebra.

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