which expression represents the area of the rectangle shown? drag and drop the the answer to the box below.
12x³ + 18x² + 9x 8x² + 18x - 14 16x² + 24x + 12 12x³ + 34x² + 15x - 12
4x² + 6x - 3
area =
3x + 4

Question

Accepted Answer

# Explanation:
## Step1: Use the area formula for a rectangle
The area $A$ of a rectangle is $A = \text{length}\times\text{width}$. Here, $\text{length}=4x^{2}+6x - 3$ and $\text{width}=3x + 4$. So, $A=(4x^{2}+6x - 3)(3x + 4)$.
## Step2: Apply the distributive property (FOIL for binomials, but extended)
$$
\begin{align*}
(4x^{2}+6x - 3)(3x + 4)&=4x^{2}(3x + 4)+6x(3x + 4)-3(3x + 4)\
&=(4x^{2}\times3x+4x^{2}\times4)+(6x\times3x + 6x\times4)+(-3\times3x-3\times4)
\end{align*}
$$
## Step3: Calculate each product
$$
\begin{align*}
4x^{2}\times3x&=12x^{3},&4x^{2}\times4&=16x^{2},\
6x\times3x&=18x^{2},&6x\times4&=24x,\
-3\times3x&=-9x,&-3\times4&=-12
\end{align*}
$$
## Step4: Combine like - terms
$$
\begin{align*}
A&=12x^{3}+16x^{2}+18x^{2}+24x-9x - 12\
&=12x^{3}+(16x^{2}+18x^{2})+(24x-9x)-12\
&=12x^{3}+34x^{2}+15x - 12
\end{align*}
$$

# Answer:
$12x^{3}+34x^{2}+15x - 12$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the area formula for a rectangle

Step2: Apply the distributive property (FOIL for binomials, but extended)

Step3: Calculate each product

Step4: Combine like - terms

Answer: