Question

Find the value of the expression r4 - 5r3 - 4r2 + 5r + 75 when r = 5.

Answer 1

To find the value of the expression \( r^4 - 5r^3 - 4r^2 + 5r + 75 \) when \( r = 5 \), we will substitute \( r = 5 \) into the expression and then perform the calculations.

First, substitute \( r = 5 \):

\[
5^4 - 5 \times 5^3 - 4 \times 5^2 + 5 \times 5 + 75
\]

Now, compute each term step by step:

1. Calculate \( 5^4 \):
\[
5^4 = 625
\]

2. Calculate \( -5 \times 5^3 \):
\[
5^3 = 125 \implies -5 \times 125 = -625
\]

3. Calculate \( -4 \times 5^2 \):
\[
5^2 = 25 \implies -4 \times 25 = -100
\]

4. Calculate \( 5 \times 5 \):
\[
5 \times 5 = 25
\]

5. The constant term is \( 75 \).

Now put it all together:

\[
625 - 625 - 100 + 25 + 75
\]

Now simplify the expression step by step:

\[
625 - 625 = 0
\]

Now add the remaining terms:

\[
0 - 100 + 25 + 75
\]

Calculate \( -100 + 25 \):

\[
-100 + 25 = -75
\]

Then add \( -75 + 75 \):

\[
-75 + 75 = 0
\]

Finally, the value of the expression when \( r = 5 \) is

\[
\boxed{0}
\]