Question

Written as a simplified polynomial in standard form, what is the result when (x + 5) ^ 2 is subtracted from 1?

Answer 1

To solve the problem, we start with \( (x + 5)^2 \) and then subtract it from 1.

First, we need to expand \( (x + 5)^2 \):

\[
(x + 5)^2 = x^2 + 2 \cdot x \cdot 5 + 5^2 = x^2 + 10x + 25
\]

Next, we subtract \( (x + 5)^2 \) from 1:

\[
1 - (x^2 + 10x + 25)
\]

Distributing the negative sign:

\[
1 - x^2 - 10x - 25
\]

Now, we combine like terms:

\[
1 - 25 - x^2 - 10x = -x^2 - 10x - 24
\]

Rearranging to write it in standard form, we get:

\[
-x^2 - 10x - 24
\]

So, the final answer is:

\[
-x^2 - 10x - 24
\]