The area of a rectangle with dimensions F+10 feet by F+5 feet is expressed as the polynomial F²+ 15F + 50. This is derived by multiplying and expanding the expressions for length and height.
The area of a rectangle can be found by multiplying its length by its height. In this case, the length of the rectangle is expressed as F + 10 feet and the height as F + 5 feet. Therefore, the area (A) of the rectangle is:
A = (F + 10)(F + 5)
To express this as a polynomial, we need to expand the expression:
A = F(F + 5) + 10(F + 5)
Distribute the terms inside the parentheses:
A = F²+ 5F + 10F + 50
Combine like terms:
A = F²+15F + 50
Thus, the area of the rectangle as a polynomial is F²+ 15F + 50.
