Answer:
C. \(6y^2+14y+81\)
Step-by-step 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.
