The expression you've provided is:

\[
5ax^2 + 5a - 15x^2 - 15
\]

Let's simplify and factor this expression.

### 1. **Factor by grouping:**

First, we can group the terms:

\[
(5ax^2 + 5a) - (15x^2 + 15)
\]

Next, factor out the common factors from each group:

- From the first group \((5ax^2 + 5a)\), factor out \(5a\):

\[
5a(x^2 + 1)
\]

- From the second group \((15x^2 + 15)\), factor out \(-15\):

\[
-15(x^2 + 1)
\]

Now, the expression becomes:

\[
5a(x^2 + 1) - 15(x^2 + 1)
\]

Finally, factor out the common binomial factor \((x^2 + 1)\):

\[
(5a - 15)(x^2 + 1)
\]

### 2. **Simplify the remaining factor:**

The expression can be simplified further by factoring \(5\) out of \((5a - 15)\):

\[
5(a - 3)(x^2 + 1)
\]

So, the fully factored form of the expression is:

\[
5(a - 3)(x^2 + 1)
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. How would you factor the expression \(4ax^2 + 4a - 8x^2 - 8\)?
2. Can you factor \(2ax^2 + 2a - 6x^2 - 6\) in a similar way?
3. What is the factored form of \(3ax^2 + 3a - 9x^2 - 9\)?
4. How do you simplify and factor \(7ax^2 + 7a - 14x^2 - 14\)?
5. Can you factor \(10ax^2 + 10a - 20x^2 - 20\)?

**Tip:** Always check if there are common factors that can be factored out from all terms before starting the grouping process.

Learn how to factor the expression 5ax^2 + 5a - 15x^2 - 15 step-by-step with detailed explanations and examples. This problem covers key algebraic concepts including factoring polynomials and is suitable for Grades 9-12 students.

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