Question

1. (06.04 mc) the length of a rectangle is represented by the function l(x)=4x. the width of that same rectangle is represented by the function w(x)=7x² - 4x + 2. which of the following shows the area of the rectangle in terms of x? (1 point) (l + w)(x)=7x² + 2 (l + w)(x)=7x² - 8x + 2 (l • w)(x)=28x³ - 16x² + 8x (l • w)(x)=28x³ - 4x + 2 21. (06.04 mc)

Explanation:

Step1: Recall area formula

The area of a rectangle $A=(L\cdot W)(x)$, where $L(x)$ is the length and $W(x)$ is the width. Given $L(x) = 4x$ and $W(x)=7x^{2}-4x + 2$.

Step2: Multiply the functions

$(L\cdot W)(x)=4x(7x^{2}-4x + 2)$.
Using the distributive property $a(b + c + d)=ab+ac + ad$, we have $4x\times7x^{2}-4x\times4x+4x\times2$.
$4x\times7x^{2}=28x^{3}$, $4x\times4x = 16x^{2}$, $4x\times2=8x$.
So, $(L\cdot W)(x)=28x^{3}-16x^{2}+8x$.

Answer:

$(L\cdot W)(x)=28x^{3}-16x^{2}+8x$