A rectangle has a height of 5y^3 and a width of 3y^3-8y^2+2y. Express the area of the entire rectangle.

A = 15y^5 - 40y^4 + 10y^3

Step-by-step explanation:

The area, A, is equal to the product of the height and the width:

A = (5y^3) (3y^3 - 8y^2 + 2y)

We can simplify the work just a lilttle by factoring out y from the second multiplicand:

A = (y) * (5y^2) * (3y^2 - 8y + 2)

Holding the (y) for last, we multiply (5y^3) * (3y^2 - 8y + 2), obtaining

A = y * (15y^4 - 40y^3 + 10 y^2

Completing this multiplication, we get the final answer:

A = 15y^5 - 40y^4 + 10y^3.