Write a simplified polynomial expression in standard form to represent the area of the rectangle below:
A picture of a rectangle is shown with one side labeled as 2 x minus 2 and another side labeled as x plus 4.
The area of a rectangle is given by the formula A = length x width. In this case, the length is 2x - 2 and the width is x + 4. Therefore, the simplified polynomial expression in standard form for the area of the rectangle is:
A = (2x - 2)(x + 4)
Expanding this expression gives:
A = 2x^2 + 6x - 8
So, the simplified polynomial expression in standard form for the area of the rectangle is 2x^2 + 6x - 8.
To find the area of a rectangle, we multiply the length by the width.
Given that the length is 2x - 2 and the width is x + 4, the expression for the area would be:
Area = (2x - 2) * (x + 4)
To simplify this expression in standard form, we can distribute and combine like terms:
Area = 2x * x + 2x * 4 - 2 * x - 2 * 4
Area = 2x^2 + 8x - 2x - 8
Combining like terms, we get:
Area = 2x^2 + 6x - 8
Therefore, the simplified polynomial expression in standard form representing the area of the rectangle is 2x^2 + 6x - 8.