Calculate Rectangle Area with Dimensions (x-2) and (x+4): Algebraic Geometry

To find the area of the given rectangle, we will multiply its length and width:

The rectangle has dimensions $x - 2$ and $x + 4$. The area formula for a rectangle is:

$\text{Area} = \text{length} \times \text{width}$

Substituting the dimensions, we get:

$\text{Area} = (x - 2)(x + 4)$

Next, we expand this expression:

$(x - 2)(x + 4) = x(x + 4) - 2(x + 4)$

The expanded terms are:

$= x^2 + 4x - 2x - 8$

Combining like terms, we obtain:

$= x^2 + 2x - 8$

Thus, the area of the rectangle is $x^2 + 2x - 8$.

In terms of the given choices, the correct choice is: $x^2 + 2x - 8$.