Question

A greenhouse that specializes in growing carnations is divided into sections. The number of plants in each section depends on the number of sprinklers in that section.

There are y(5y − 4) red carnation plants and (9 + y)2 white carnation plants in a section with y sprinklers.

Which simplified expression represents the total number of red and white carnation plants in a section with y sprinklers?
5y2 + 18y +77
5y4 + 14y + 81
6y2 + 14y + 81
6y2 + 18y + 77

Answer 1

Good evening,

y(5y-4)+(9+y)²=5y²-4y+81+18y+y²
=6y²+14y+81

Answer 2

C.
`6y^2+14y+81`

Explanation:

We have been given that the expression
`y(5y-4)` represents number of red carnation plants and expression
`(9+y)^2` represents number of white carnation plants in a section with y sprinklers in a green house.

To find the simplified expression that represents the total number of red and white carnation plants in a section with y sprinklers, we will add our both expressions.

`y(5y-4)+(9+y)^2`

Upon distributing y on 1st expression we will get,

`5y*y-4y+(9+y)^2`

`5y^2-4y+(9+y)^2`

Upon expanding the perfect square we will get,

`5y^2-4y+(9^2+2*9y+y^2)`

`5y^2-4y+(81+18y+y^2)`

`5y^2-4y+81+18y+y^2`

Now, we will combine like terms.

`5y^2+y^2-4y+18y+81`

`6y^2+14y+81`

Therefore, option C is the correct choice.