Question

Evaluate the expression for n = –9 and p = 3. Simplify your answer.

n2 + np
p2
=

Answer 1

To evaluate the expression \( \frac{n^2 + np}{p^2} \) for \( n = -9 \) and \( p = 3 \), we can follow these steps:

1. Calculate \( n^2 \):
\[
n^2 = (-9)^2 = 81
\]

2. Calculate \( np \):
\[
np = (-9)(3) = -27
\]

3. Substitute \( n^2 \) and \( np \) into the expression:
\[
n^2 + np = 81 - 27 = 54
\]

4. Calculate \( p^2 \):
\[
p^2 = 3^2 = 9
\]

5. Substitute \( n^2 + np \) and \( p^2 \) into the expression:
\[
\frac{n^2 + np}{p^2} = \frac{54}{9}
\]

6. Simplify the fraction:
\[
\frac{54}{9} = 6
\]

The final result is:
\[
\boxed{6}
\]