Question

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) = 7x^{2}-4x + 2 ). which of the following shows the area of the rectangle in terms of ( x )?
( \bigcirc (l + w)(x)=7x^{2}+2 )
( \bigcirc (lcdot w)(x)=28x^{3}-16x^{2}+8x )
( \bigcirc (l + w)(x)=7x^{2}-8x + 2 )
( \bigcirc (lcdot w)(x)=28x^{3}-4x + 2 )

Explanation:

Step1: Recall the area formula for a rectangle

The area \(A\) of a rectangle is \(A = L\times W\) (where \(L\) is length and \(W\) is width). So we need to find \((L\cdot W)(x)\)

Step2: Substitute the given functions

Given \(L(x)=4x\) and \(W(x)=7x^{2}-4x + 2\), then \((L\cdot W)(x)=4x(7x^{2}-4x + 2)\)

Step3: Use the distributive property \(a(b + c+d)=ab+ac + ad\)

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Answer:

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