To simplify the expression \((r + 7)(r - 8)\), you can use the distributive property (also known as the FOIL method for binomials):

\[
(r + 7)(r - 8) = r \cdot r + r \cdot (-8) + 7 \cdot r + 7 \cdot (-8)
\]

Now, let's simplify each term:

- \(r \cdot r = r^2\)
- \(r \cdot (-8) = -8r\)
- \(7 \cdot r = 7r\)
- \(7 \cdot (-8) = -56\)

Now, combine all the terms:

\[
r^2 - 8r + 7r - 56
\]

Combine the like terms \(-8r\) and \(7r\):

\[
r^2 - r - 56
\]

So, the simplified form of \((r + 7)(r - 8)\) is:

\[
r^2 - r - 56
\]

Would you like more details, or do you have any questions?

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Here are 8 related questions:

1. How would you expand \((r + 3)(r + 4)\)?
2. What is the result of \((r - 6)(r + 2)\)?
3. How would you simplify \((2r + 5)(r - 7)\)?
4. What happens when you expand \((r - 9)(r + 1)\)?
5. Can you factor the expression \(r^2 - r - 56\) back into binomials?
6. How does the distributive property apply to expanding binomials?
7. What is the difference between expanding and factoring in algebra?
8. How would you expand a trinomial expression like \((r + 2)(r^2 - 3r + 5)\)?

**Tip:** Always combine like terms after expanding expressions to ensure the simplest form of your answer.

Learn how to simplify the expression (r + 7)(r - 8) with a detailed step-by-step solution using the distributive property. This problem covers algebraic concepts such as the distributive property and binomials, suitable for Grades 7-9 students.

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