To solve the expression \( p^2 - 5q + r^2 \) with the given values \( p = -5 \), \( q = 6 \), and \( r = -10 \), we substitute the values into the expression:

\[
(-5)^2 - 5(6) + (-10)^2
\]

Now, let's calculate each part:

1. \( (-5)^2 = 25 \)
2. \( 5(6) = 30 \)
3. \( (-10)^2 = 100 \)

Substitute these back into the expression:

\[
25 - 30 + 100
\]

Now, simplify it:

\[
25 - 30 = -5
\]
\[
-5 + 100 = 95
\]

So, the value of the expression is **95**.

Would you like details on any step, or do you have any other questions? Here are 5 related questions for further practice:

1. What is the value of the expression \( p^2 + 5q + r^2 \) with the same values of \( p \), \( q \), and \( r \)?
2. How does the result change if \( p = 0 \)?
3. What happens if \( q \) is negative in the expression?
4. How would the expression change if we added a \( pq \) term?
5. Calculate the expression \( p^2 - 5q + r^2 \) when \( p = 2 \), \( q = -4 \), and \( r = 3 \).

**Tip:** When substituting negative values into an expression, remember to carefully square or multiply them to avoid sign errors.

Learn how to solve the expression p^2 - 5q + r^2 with the values p = -5, q = 6, and r = -10. This problem involves substituting values into a quadratic-like expression and performing calculations step-by-step. Suitable for students studying algebra and quadratic equations in Grades 7-9.

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