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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?

Verified Answer :

The solution would be like
this for this specific problem:

y(5y − 4) + (9 + y)²

Simplify the expression:

(5y² −
4y) + (81 + 18y + y²) 

Combine the like terms:

6y² +
14y + 81

The simplified expression that
represents the total number of red and white carnation plants in a section with
y sprinklers is 6y² + 14y +

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Answer:

The required equation is  \(T=6y^2+14y+81\)

Step-by-step explanation:

Given : 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.

Red carnation plants = \(y(5y-4)\)

White carnation plants = \((9+y)^2\)

with y sprinklers.

To find : Which simplified expression represents the total number of red and white carnation plants in a section with y sprinklers?

Solution :

Total number = Red carnation + White carnation plants

\(T=y(5y-4)+(9+y)^2\)

Now, we solve the equation

\(T=5y^2-4y+9^2+y^2+2\cdot 9\cdot y\)

\(T=5y^2-4y+81+y^2+18y\)

\(T=6y^2+14y+81\)

Therefore, The required equation is  \(T=6y^2+14y+81\)

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