Question

what is the area of this rectangle? 2x² + 6x + 8; 8x² + 14x + 6; 8x² + x + 5; 48 (rectangle with length 4x + 3 and width 2x + 2)

Explanation:

Step1: Recall the area formula for a rectangle

The area \(A\) of a rectangle is given by the product of its length and width, i.e., \(A=\text{length}\times\text{width}\). Here, the length is \(4x + 3\) and the width is \(2x+2\). So we need to calculate \((4x + 3)(2x + 2)\).

Step2: Apply the distributive property (FOIL method)

First, multiply the First terms: \(4x\times2x = 8x^{2}\).
Then, multiply the Outer terms: \(4x\times2=8x\).
Next, multiply the Inner terms: \(3\times2x = 6x\).
Finally, multiply the Last terms: \(3\times2 = 6\).

Step3: Combine like terms

Now, add up all the terms: \(8x^{2}+8x + 6x+6\). Combining the like terms \(8x\) and \(6x\) (since they are both linear terms in \(x\)), we get \(8x^{2}+(8x + 6x)+6=8x^{2}+14x + 6\).

Answer:

\(8x^{2}+14x + 6\)