Sure, let's go through this step-by-step to find the area of the rectangle.
1. We are given that the height of the rectangle is [tex]\(5\)[/tex].
2. We are also given that the width of the rectangle is [tex]\(4x^2 - 2x - 6\)[/tex].
To find the area of the rectangle, we use the formula:
[tex]\[
\text{Area} = \text{Height} \times \text{Width}
\][/tex]
3. Substituting the given height and width into the formula, we get:
[tex]\[
\text{Area} = 5 \times (4x^2 - 2x - 6)
\][/tex]
4. Now, we need to distribute the [tex]\(5\)[/tex] to each term inside the parentheses:
[tex]\[
\text{Area} = 5 \times 4x^2 + 5 \times (-2x) + 5 \times (-6)
\][/tex]
5. Performing the multiplication yields:
[tex]\[
\text{Area} = 20x^2 - 10x - 30
\][/tex]
So, the expanded expression for the area of the rectangle is:
[tex]\[
\text{Area} = 20x^2 - 10x - 30
\][/tex]
