Answer:
Option D is correct.
\((L \cdot W)(x) = 16x^3-8x^2+2x\)
Step-by-step 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:
\((L \cdot W)(x) = 16x^3-8x^2+2x\)
