Question

The length of a rectangle is represented by the function L(x) = 2x. The width of that same rectangle is represented by the function W(x) = 8x2 − 4x + 1. Which of the following shows the area of the rectangle in terms of x?

(L + W)(x) = 8x2 − 2x + 1
(L + W)(x) = 8x2 − 6x + 1
(L ⋅ W)(x) = 16x3 − 4x + 1
(L ⋅ W)(x) = 16x3 − 8x2 + 2x

Answer 1

Area of a rectangle = length * width = (2x) *
`8x^(2) - 4x + 1` =
`16 x^(3) - 8 x^(2) + 2x`

Answer: the last option

Answer 2

Option D is correct.

`(L \cdot W)(x) = 16x^3-8x^2+2x`

Explanation:

Area of rectangle(A) is given by:

`A = l \cdot w`

where

l is the length of rectangle and w is the width of the rectangle respectively.

As per the statement:

Length of a rectangle L(x) = 2x and

Width of a rectangle W(x) =
`8x^2-4x+1`

Then by formula of area of rectangle:

`A(x) = L(x) \cdot W(x) = (L \cdot W)(x)`

Substitute the given values we have;

`(L \cdot W)(x) = (2x) \cdot (8x^2-4x+1)`

Using the distributive property:
`a\ cdot (b+c) = a\cdot b+a\cdot c`

`(L \cdot W)(x) = 16x^3-8x^2+2x`

Therefore, the area of the rectangle in terms of x is:

`(L \cdot W)(x) = 16x^3-8x^2+2x`