Question

the side lengths of a rectangle are described as (8a + 1) feet and (3a - 2) feet. which expression represents the area of the rectangle in square feet?

1. (11a^{2}+13a - 2)
2. (11a^{2}+19a - 2)
3. (24a^{2}+19a - 2)
4. (24a^{2}-13a - 2)

Explanation:

Step1: Recall area formula for rectangle

The area $A$ of a rectangle is given by $A = l\times w$, where $l$ and $w$ are the length and width. Here, $l=(8a + 1)$ and $w=(3a-2)$.

Step2: Multiply the two binomials

Using the FOIL method:
\[

$$\begin{align*} (8a + 1)(3a-2)&=8a\times3a+8a\times(-2)+1\times3a + 1\times(-2)\\ &=24a^{2}-16a + 3a-2\\ &=24a^{2}-13a - 2 \end{align*}$$

\]

Answer:

$24a^{2}-13a - 2$ (corresponding to the last option in the multiple - choice list)