Question

a rectangular garden has dimensions (x + 4) by (x - 4). if a 2x2 square is removed from one corner, what expression represents the remaining area?

Answer 1

To find the area of the rectangular garden after removing a 2x2 square from one corner, we first need to calculate the area of the original rectangle and then subtract the area of the square that is removed.

1. **Calculate the area of the rectangle**:
The dimensions of the rectangle are \((x + 4)\) and \((x - 4)\).
\[
\text{Area of the rectangle} = (x + 4)(x - 4)
\]
We can use the difference of squares formula to simplify this:
\[
(x + 4)(x - 4) = x^2 - 16
\]

2. **Calculate the area of the square that is removed**:
The area of the 2x2 square is:
\[
\text{Area of the square} = 2 \times 2 = 4
\]

3. **Calculate the remaining area**:
We subtract the area of the square from the area of the rectangle:
\[
\text{Remaining area} = \text{Area of the rectangle} - \text{Area of the square}
\]
Substituting in our expressions:
\[
\text{Remaining area} = (x^2 - 16) - 4
\]
Simplifying further, we get:
\[
\text{Remaining area} = x^2 - 16 - 4 = x^2 - 20
\]

Thus, the expression that represents the remaining area of the garden after removing the 2x2 square is:
\[
\boxed{x^2 - 20}
\]