Question

A rectangle has a height of (m + 8) and a width of (2m^3 + m^2 + 3m).

- a) (2m^4 + m^3 + 11m^2 + 27m + 24)
- b) (2m^4 + m^3 + 11m^2 + 27m + 21)
- c) (2m^4 + m^3 + 11m^2 + 27m + 18)
- d) (2m^4 + m^3 + 11m^2 + 27m + 15)

Answer 1

To calculate the area of the rectangle with height (m + 8) and width (2m^3 + m^2 + 3m), we expand the expression and combine like terms to get 2m^4 + 17m^3 + 11m^2 + 24m, which does not match any of the provided options.

Step-by-step explanation:

To find the area of a rectangle, we multiply its height by its width. Given a height of (m + 8) and a width of (2m^3 + m^2 + 3m), we need to apply the distributive property to perform the multiplication:

Area = (m + 8)(2m^3 + m^2 + 3m)

Expanding the expression:

• m × 2m^3 = 2m^4
• m × m^2 = m^3
• m × 3m = 3m^2
• 8 × 2m^3 = 16m^3
• 8 × m^2 = 8m^2
• 8 × 3m = 24m

Adding these together, we get:

Area = 2m^4 + m^3 + 16m^3 + 3m^2 + 8m^2 + 24m

Combine like terms:

Area = 2m^4 + 17m^3 + 11m^2 + 24m

This is not one of the options provided, which suggests a typo in the options or the need to review the original problem statement for errors.