A rectangle has a height of 5 and a width of [tex]4x^2 - 2x - 6[/tex].

Express the area of the entire rectangle.

The expression should be expanded.

Area [tex]= \square[/tex]



Answer :

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]