Let's simplify the expression:

Given:

\[
5(r^2 - 5r - 1)
\]

Distribute the 5 across the terms inside the parentheses:

\[
5 \times r^2 - 5 \times 5r - 5 \times 1
\]

This simplifies to:

\[
5r^2 - 25r - 5
\]

So, the simplified expression is:

\[
5r^2 - 25r - 5
\]

Would you like any further details or have any questions about this problem?

Here are 5 related questions you might find interesting:
1. How would you factor the expression \(5r^2 - 25r - 5\)?
2. What is the value of the expression if \(r = 3\)?
3. Can you find the roots of the equation \(5r^2 - 25r - 5 = 0\)?
4. How would you complete the square for the expression \(5r^2 - 25r - 5\)?
5. How does the expression change if you add 10 to the entire equation?

**Tip:** When distributing a factor across terms inside parentheses, remember to multiply each term inside by that factor.

Learn how to simplify the polynomial expression 5(r^2 - 5r - 1) by applying the distributive property. This step-by-step guide covers essential algebraic concepts such as polynomial expansion and simplification. Suitable for students in Grades 8-10.

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