Write an algebraic expression to represent the area of the shaded region.

4y^{2}+3y

Step-by-step explanation:

First you need to distribute the values.    

(4y+3)(2y) Using the "Rainbow Method" to multiply the polynomials    

You Should get    

8y^{2}+6y    

Since this is the area of the rectangle and we need to find the area of the shaded region you need to dived 8y^{2}+6y in half because the shaded region is half of the rectangle.    

8y^{2}+6y/2    

Doing this you will get    

4y^{2}+3y