The dimensions of a rectangular garden in feet are (3m + 7) and (2m + 8), where m is a positive integer. Which expression represents the area of the garden in square feet?
A.) 6m^2 + 14m + 56
B.) 5m^2 + 15
C.) 6m^2 + 38m + 56
D.) 5m^2 + 56
To find the area of a rectangle, multiply the length by the width.
In this case, the length is (3m + 7) and the width is (2m + 8).
Therefore, the area is (3m + 7) * (2m + 8).
To find the product of these binomials, you can use the distributive property.
(3m + 7) * (2m + 8) = 3m * 2m + 3m * 8 + 7 * 2m + 7 * 8
Simplifying this expression gives us:
6m^2 + 24m + 14m + 56
Combining like terms, we get:
6m^2 + 38m + 56
Therefore, the expression that represents the area of the garden in square feet is C.) 6m^2 + 38m + 56.