A rectangle has a height of 2y^3+52y
3
+52, y, cubed, plus, 5 and a width of y^3+6yy
3
+6yy, cubed, plus, 6, y.
Express the area of the entire rectangle.
Your answer should be a polynomial in standard form.

9514 1404 393

  2y^6 +12y^4 +5y^3 +30y

Step-by-step explanation:

Given:

  rectangle height: 2y^3 +5

  and width: y^3+6y

Find:

  the area as a polynomial

Solution:

  The area is the product of height and width:

  A = (2y^3 +5)(y^3 +6y)

  A = (2y^3)(y^3 +6y) +5(y^3 +6y)

  A = 2y^6 +12y^4 +5y^3 +30y . . . . area of the rectangle