Question

The length of a rectangle is represented by (6x − 2), and the width is represented by (x − 1). Which expression best represents the area of the rectangle?

A)6x^2 - 8x + 2.
B)5x^2 - 3x + 1
C)4x^2 - 1x + 2.
D)2x^2 - 9x + 2.

Answer 1

The area of a rectangle with length (6x - 2) and width (x - 1) is found by multiplying the two expressions, resulting in an area of 6x^2 - 8x + 2.

Step-by-step explanation:

Finding the Area of a Rectangle with Algebraic Expressions

To find the area of a rectangle, you multiply its length by its width. In this case, the length is (6x - 2) and the width is (x - 1). So to find the area, we'll use the following expression:

Area = length × width = (6x - 2)(x - 1)

Now we need to expand this expression:

Area = 6x(x) + 6x(-1) - 2(x) - 2(-1)

Area = 6x^2 - 6x - 2x + 2

Area = 6x^2 - 8x + 2

Therefore, the expression that best represents the area of the rectangle is 6x^2 - 8x + 2, which corresponds to option A.