Question

13 a rectangle has side lengths of (3x - 2) and (2x + 2). write an expression in standard form that represents the area of the rectangle. a $6x^{2}+2x - 4$ b $5x^{2}+2x - 4$ c $6x^{2}-2x + 4$ d $5x^{2}-2x - 4$

Explanation:

Step1: Use the area formula for a rectangle

The area \(A\) of a rectangle is \(A = l\times w\), where \(l=(3x - 2)\) and \(w=(2x + 2)\). So \(A=(3x - 2)(2x + 2)\).

Step2: Apply the distributive property (FOIL method)

$$
LATEXBLOCK0
$$

Step3: Combine like terms

\(6x^{2}+(6x - 4x)-4=6x^{2}+2x - 4\)

Answer:

A. \(6x^{2}+2x - 4\)