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

Look at the rectangle in the figure.

What is its area?

x-2x+4

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's calculate the area of this rectangle.
00:09 We will use the formula for the area of a rectangle: length times width.
00:17 First, let's make sure to open those parentheses. Each number will multiply with the other.
00:42 Now, let's do the math to find the products.
00:55 Next, we group the numbers together.
01:00 And that is how we find the solution to our problem!

Step-by-step written solution

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1

Understand the problem

Look at the rectangle in the figure.

What is its area?

x-2x+4

2

Step-by-step solution

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

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

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

Substituting the dimensions, we get:

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

Next, we expand this expression:

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

The expanded terms are:

=x2+4x−2x−8 = x^2 + 4x - 2x - 8

Combining like terms, we obtain:

=x2+2x−8 = x^2 + 2x - 8

Thus, the area of the rectangle is x2+2x−8x^2 + 2x - 8.

In terms of the given choices, the correct choice is: x2+2x−8 x^2 + 2x - 8 .

3

Final Answer

x2+2x−8 x^2+2x-8

Practice Quiz

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Solve the following expression:

\( x^2-1=0 \)

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