Which of the following expressions represents the difference in terms of y, between the area of thw triangle and the area of the rectangle

Hello,

Start by writing out the area formula's for both a triangle and a rectangle.
Triangle: Area=(1/2)Base x Height **Call this area A(T)
Rectangle: Area=Base x Height **Call this area A(R)

Ultimately, we are trying to find the difference between the two so A(T) - A(R) = ?

Start by finding the A(T). We are given that the base=(3y-1) and the height=6y.  According to our formula above, A(T)=(1/2)(3y-1)(6y).  Once you foil this all out you get A(T)=9y^2 -3y

Next, find A(R).  Again, follow the formula from above with the given info from the problem.  A(R)=(5y-7)(y+4).  Foil this out and combine like terms to get A(R)=5y^2 +13y-28

Now we can subtract the two and find that A(T) - A(R) = 4y^2 + 10y - 28.  Or answer D.