Question

The sides of an outer square is x + 5. An inner square has sides of 2. Write a polynomial that describes the area of the outer square.

Answer 1

To find the area of the outer square, we need to use the formula for the area of a square, which is given by:

\[
\text{Area} = \text{side length}^2
\]

In this case, the side length of the outer square is given as \(x + 5\). Thus, to find the area of the outer square, we can substitute \(x + 5\) into the area formula:

\[
\text{Area of outer square} = (x + 5)^2
\]

Next, we expand the polynomial:

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

Therefore, the polynomial that describes the area of the outer square is:

\[
\boxed{x^2 + 10x + 25}
\]